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The aim of this paper is to provide a survey of the state of the art in the finite element approach to the Immersed Boundary Method (FE-IBM) which has been investigated by the authors during the last decade. In a unified setting, we present the different formulation proposed in our research and highlight the advantages of the one based on a distributed Lagrange multiplier (DLM-IBM) over the original FE-IBM.

Book Source: Digital Library of India Item 2015.228596 dc.contributor.author: M. G. Rajasekaran dc.date.accessioned: 2015-07-10T15:50:49Z dc.date.available: 2015-07-10T15:50:49Z dc.date.digitalpublicationdate: 0000-00-00 dc.identifier.barcode: 5990010123915 dc.identifier.origpath: /rawdataupload/upload/0123/918 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/228596 dc.description.scanningcentre: IIIT, Allahabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 64 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher: Iit Kanpur dc.rights: Out_of_copyright dc.source.library: I I T Kanpur dc.subject.classification: Technology dc.subject.classification: Engineering. Technology In General dc.subject.classification: Mechanical Engineering In General. Nuclear Technology. Electrical Engineering. Machinery dc.title: Stresses In Plates With A Hole Using Boundary Element Method

We consider the P1/P1 or P1b/P1 finite element approximations to the Stokes equations in a bounded smooth domain subject to the slip boundary condition. A penalty method is applied to address the essential boundary condition $u\cdot n = g$ on $\partial\Omega$, which avoids a variational crime and simultaneously facilitates the numerical implementation. We give $O(h^{1/2} + \epsilon^{1/2} + h/\epsilon^{1/2})$-error estimate for velocity and pressure in the energy norm, where $h$ and $\epsilon$ denote the discretization parameter and the penalty parameter, respectively. In the two-dimensional case, it is improved to $O(h + \epsilon^{1/2} + h^2/\epsilon^{1/2})$ by applying reduced-order numerical integration to the penalty term. The theoretical results are confirmed by numerical experiments.

The CVBEM is used to develop a computer model for estimating the location of the freezing front in soil-water phase change problems. The CVBFR1 computer program is based on the following major assumptions: 1) the problem is two-dimensional; 2) the entire soil system is homogeneous and isotropic; 3) the problem thermal boundary conditions are constant values of temperature (or stream function); 4) soil water flow effects are neglected (the problem is strictly geothermal); 5)all heat flow from the freezing front is within the control volume, there is no heat flux associated with the freezing front from exterior of the control volume; and 6) the freezing front movement is slow enough that heat flux along the moving boundary can be determined by assuming steady state heat flow conditions for small durations of time (i.e., timesteps). The CVBEM is used to model the thermal regime of the soil system. The theory and development of the CVBEM are given in CRREL internal report 969, by Hromadka. Because the numerical technique is a boundary integral approach, the control volume thermal regime is modeled with respect to the boundary values, and, therefore, the CVBFR1 data entry requirements are significantly less than those usually required of domain methods. Soil-water phase change along the freezing front is modeled as a simple balance between computed heat flux and evolution of soil-water volumetric latent heat of fusion. To model displacement of the freezing front, program CVBFR1 provides two options: displace the freezing front coordinates with respect to changes in the y-coordinate only, or with respect to a vector normal to the freezing front boundary.

The long-range scientific goals are (1) to understand the basic physics of acoustic scattering by fish targets, and (2) to apply forthcoming knowledge over a broad frequency range in order to be able to differentiate fish from non-fish targets.

The long-range scientific goals are (1) to understand the basic physics of acoustic scattering by fish targets, and (2) to apply forthcoming knowledge over a broad frequency range in order to be able to differentiate fish from non-fish targets.

Dynamical energy analysis was recently introduced as a new method for determining the distribution of mechanical and acoustic wave energy in complex built up structures. The technique interpolates between standard statistical energy analysis and full ray tracing, containing both of these methods as limiting cases. As such the applicability of the method is wide ranging and additionally includes the numerical modelling of problems in optics and more generally of linear wave problems in electromagnetics. In this work we consider a new approach to the method with enhanced versatility, enabling three-dimensional problems to be handled in a straightforward manner. The main challenge is the high dimensionality of the problem: we determine the wave energy density both as a function of the spatial coordinate and momentum (or direction) space. The momentum variables are expressed in separable (polar) coordinates facilitating the use of products of univariate basis expansions. However this is not the case for the spatial argument and so we propose to make use of automated mesh generating routines to both localise the approximation, allowing quadrature costs to be kept moderate, and give versatility in the code for different geometric configurations.

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Fast surface integral equation (SIE) solvers seem to be ideal approaches for simulating 3-D nanophotonic devices, as these devices generate fields both in an interior channel and in the infinite exterior domain. However, many devices of interest, such as optical couplers, have channels that can not be terminated without generating reflections. Generating absorbers for these channels is a new problem for SIE methods, as the methods were initially developed for problems with finite surfaces. In this paper we show that the obvious approach for eliminating reflections, making the channel mildly conductive outside the domain of interest, is inaccurate. We describe a new method, in which the absorber has a gradually increasing surface conductivity; such an absorber can be easily incorporated in fast integral equation solvers. Numerical experiments from a surface-conductivity modified FFT-accelerated PMCHW-based solver are correlated with analytic results, demonstrating that this new method is orders of magnitude more effective than a volume absorber, and that the smoothness of the surface conductivity function determines the performance of the absorber. In particular, we show that the magnitude of the transition reflection is proportional to 1/L^(2d+2), where L is the absorber length and d is the order of the differentiability of the surface conductivity function.

The experimental realization of dynamo excitation as well as theoretical and numerical examinations of the induction equation have shown the relevance of boundary conditions for a self-sustaining dynamo. Within the interior of a field producing domain geometric constraints or varying material properties (e.g. electrical conductivity of the container walls or localized high-permeability material) might also play a role. Combining a grid based finite volume approach with the boundary element method in a hybrid FV-BEM scheme offers the flexibility of a local discretization with a stringent treatment of insulating magnetic boundary conditions in almost arbitrary geometries at comparatively low costs. Kinematic simulations of dynamo action generated by a well known prescribed mean flow demonstrate the reliability of the approach. Future examinations are intended to understand the behavior of the VKS-dynamo experiment where the field producing flow is driven by ferrous propellers and the induction effects of conductivity/permeability inhomogeneities might provide the required conditions for the measured dynamo characteristics.

We consider an interface problem often arising in transport problems: a coupled system of partial differential equations with one (elliptic) transport equation on a bounded domain and one equation (in this case the Laplace problem) on the complement, an unbounded domain. Based on the non-symmetric coupling of the finite volume method and boundary element method of [Erath et al., arXiv:1509.00440, 2015] we introduce a robust residual error estimator. The upper bound of the error in an energy (semi)norm is robust against variation of the model data. The lower bound, however, additionally depends on the Peclet number. In several examples we use the local contributions of the a~posteriori error estimator to steer an adaptive mesh-refining algorithm. The adaptive FVM-BEM coupling turns out to be an efficient method especially to solve problems from fluid mechanics, mainly because of the local flux conservation and the stable approximation of convection dominated problems.

An unsteady three-dimensional boundary element method is developed to provide fast calculations of biological and bio-inspired self-propelled locomotion. The approach uniquely combines an unsteady three-dimensional boundary element method, a boundary layer solver and self-propelled equations of motion. This novel implementation allows for the self-propelled speed, power, efficiency and economy to be accurately calculated. A Dirichlet formulation is used with a combination of constant strength source and doublet elements to represent a deforming body with a nonlinearly deforming wake. The wake elements are desingularized to numerically stabilize the evolution of the wake vorticity. Weak coupling is used in solving the equations of motion and in the boundary layer solution. The boundary layer solver models both laminar and turbulent behavior along the deforming body to estimate the total skin friction drag acting on the body. The results from the method are validated with analytical solutions, computations and experiments. Finally, a bio-inspired self-propelled undulatory fin is modeled. The computed self-propelled speeds and wake structures agree well with previous experiments. The computations go beyond the experiments to gain further insight into the propulsive efficiency for self-propelled undulating fins. It is found that the undulating fin produces a time-averaged momentum jet at 76% of the span that accelerates fluid in the streamwise direction and in turn generates thrust. Additionally, it is discovered that high amplitude motions suppress the formation of a bifurcating momentum jet and instead form a single core jet. Consequently, this maximizes the amount of streamwise momentum compared to the amount of wasted lateral momentum and leads to a propulsive efficiency of 78% during self-propelled locomotion.

The concept of isogeometric analysis, whereby the parametric func- tions that are used to describe CAD geometry are also used to approx- imate the unknown fields in a numerical discretisation, has progressed rapidly in recent years. This paper advances the field further by outlin- ing an isogeometric Boundary Element Method (IGABEM) that only re- quires a representation of the geometry of the domain for analysis, fitting neatly with the boundary representation provided completely by CAD. The method circumvents the requirement to generate a boundary mesh representing a significant step in reducing the gap between engineering design and analysis. The current paper focuses on implementation details of 2D IGABEM for elastostatic analysis with particular attention paid towards the differences over conventional boundary element implementa- tions. Examples of Matlab R{\deg} code are given whenever possible to aid understanding of the techniques used.

We introduce a new formulation for the finite element immersed boundary method which makes use of a distributed Lagrange multiplier. We prove that a full discretization of our model, based on a semi-implicit time advancing scheme, is unconditionally stable with respect to the time step size.

The Finite Element Methods was used to solve the nonlinear electron plasma equations for the System-Generated Electromagnetic Pulse boundary layer in one spatial dimension. These equations were solved in distance-velocity phase space using a rectangular finite element mesh. Linear approximations were used for both the trial and weight functions for each element. The advection terms in the Vlasov plasma equation were treated with the Heinrich upwinding technique. The time integration was performed using an explicit two-step Lax-Wendroff procedure. The system of algebraic equations were solved with a fully-packed Gauss-Seidel iteration scheme. A value of 2/3 for the upwinding parameter was found to provide the best compromise between dispersion of the pulse, and computer storage requirements. The savings in computer memory results in increased execution speed for the algorithm. Also, it is shown that the numerical scheme does not permit spurious pulse reflections from the edges of the mesh. Results for several test cases are presented. Comparisons are given which show favorable agreement for the finite element technique with other solution relationships.

This report presents a study of the indirect boundary element method and its potential advantages for solving one- and two-dimensional linear structural/stress analysis problems. The theoretical formulation of the indirect boundary element method is illustrated first by developing the framework of one-dimensional beams resting on elastic foundations, and then extending the same concept to the framework of two-dimensional plane stress or plane strain elastostatics. Computer programs were written both in BASIC and FORTRAN that numerically implement the theoretical application is written in FORTRAN. Accuracy of the indirect boundary element solution is assessed through comparison with theoretical solutions and with solutions from the alternative, direct boundary element method. With regard to edge effects, the implementation that was available for comparison. The results pertaining to the accuracy of the indirect boundary element method to correctly capture stress gradients were very encouraging, even for the constant stress elements employed. The results suggest that the method may be a very economical analysis tool for determining stress concentration factors in elastostatics. Because the necessary input data requirements are less and smaller matrices result, the boundary element methods are more suited to small computers, thus enhancing the use of the methods as effective stress analysis tools. (Author)

The objective is to further develop LAMP-QBEM, an efficient computational tool for the prediction of large amplitude ship motions and hydrodynamic loads. The key developments in this study include handling of complicated ship geometry and the development of a stable, accurate and efficient algorithm for free-surface time integration.

A method was developed to predict sound fields in acoustical cavities. The method is based on the indirect boundary element method. An isoparametric quadratic boundary element is incorporated. Pressure, velocity and/or impedance boundary conditions may be applied to a cavity by using this method. The capability to include acoustic point sources within the cavity is implemented. The method is applied to the prediction of sound fields in spherical and rectangular cavities. All three boundary condition types are verified. Cases with a point source within the cavity domain are also studied. Numerically determined cavity pressure distributions and responses are presented. The numerical results correlate well with available analytical results.

Recently, a combined approach of CFIE--BAE has been proposed by authors for solving external scattering problems in acoustics. CFIE stands for combined-field integral equations, and BAE is the method of boundary algebraical equation. The combined method is, essentially, a discrete analogue of the boundary element method (BEM), having none of its disadvantages. Namely, due to the discrete nature of BAE one should not compute quadratures of oversingular integrals. Moreover, due to CFIE formulation, the method does not possess spurious resonances. However, the CFIE--BAE method has an important drawback. Since the modelling is performed in a regular discrete space, the shape of the obstacle should be assembled of elementary "bricks", so smooth scatterers (like spheres, cylinders, etc) are approximated with a poor accuracy. This loss of accuracy becomes the bottleneck of the method. Here this disadvantage is overcome. The CFIE--BAE method developed for regular meshing of the outer space is coupled in a standard way with a relatively small irregular mesh enabling one to describe the shape of the obstacle accurately enough.

In this paper, we couple regularization techniques with the adaptive $hp$-version of the boundary element method ($hp$-BEM) for the efficient numerical solution of linear elastic problems with nonmonotone contact boundary conditions. As a model example we treat the delamination of composite structures with a contaminated interface layer. This problem has a weak formulation in terms of a nonsmooth variational inequality. The resulting hemivariational inequality (HVI) is first regularized and then, discretized by an adaptive $hp$-BEM. We give conditions for the uniqueness of the solution and provide an a-priori error estimate. Furthermore, we derive an a-posteriori error estimate for the nonsmooth variational problem based on a novel regularized mixed formulation, thus enabling $hp$-adaptivity. Various numerical experiments illustrate the behavior, strengths and weaknesses of the proposed high-order approximation scheme.

In this paper, we couple regularization techniques with the adaptive $hp$-version of the boundary element method ($hp$-BEM) for the efficient numerical solution of linear elastic problems with nonmonotone contact boundary conditions. As a model example we treat the delamination of composite structures with a contaminated interface layer. This problem has a weak formulation in terms of a nonsmooth variational inequality. The resulting hemivariational inequality (HVI) is first regularized and then, discretized by an adaptive $hp$-BEM. We give conditions for the uniqueness of the solution and provide an a-priori error estimate. Furthermore, we derive an a-posteriori error estimate for the nonsmooth variational problem based on a novel regularized mixed formulation, thus enabling $hp$-adaptivity. Various numerical experiments illustrate the behavior, strengths and weaknesses of the proposed high-order approximation scheme.

A review of a hybrid finite element-boundary integral formulation for scattering and radiation by two- and three-dimensional composite structures is presented. In contrast to other hybrid techniques involving the finite element method, the proposed one is in principle exact and can be implemented using a low O(N) storage. This is of particular importance for large scale applications and is a characteristic of the boundary chosen to terminate the finite element mesh, usually as close to the structure as possible. A certain class of these boundaries lead to convolutional boundary integrals which can be evaluated via the fast Fourier transform (FFT) without a need to generate a matrix; thus, retaining the O(N) storage requirement. The paper begins with a general description of the method. A number of two- and three-dimensional applications are then given, including numerical computations which demonstrate the method's accuracy, efficiency, and capability.

A review of a hybrid finite element-boundary integral formulation for scattering and radiation by two- and three-dimensional composite structures is presented. In contrast to other hybrid techniques involving the finite element method, the proposed one is in principle exact and can be implemented using a low O(N) storage. This is of particular importance for large scale applications and is a characteristic of the boundary chosen to terminate the finite element mesh, usually as close to the structure as possible. A certain class of these boundaries lead to convolutional boundary integrals which can be evaluated via the fast Fourier transform (FFT) without a need to generate a matrix; thus, retaining the O(N) storage requirement. The paper begins with a general description of the method. A number of two- and three-dimensional applications are then given, including numerical computations which demonstrate the method's accuracy, efficiency, and capability.

This thesis considers problems for which the boundary is not known before the problem is solved and must be determined as part of the solution. We consider a time dependent problem which results in a moving boundary. We look at the heat conduction/diffusion equation in one and two spatial dimensions. We use Green's Theorem to yield a Volterra boundary integral equation which involves an unknown function on the moving boundary. We use the boundary element method to obtain a solution. Graphical results for the two dimensional problem are presented.

The Finite Element Methods was used to solve the nonlinear electron plasma equations for the System-Generated Electromagnetic Pulse boundary layer in one spatial dimension. These equations were solved in distance-velocity phase space using a rectangular finite element mesh. Linear approximations were used for both the trial and weight functions for each element. The advection terms in the Vlasov plasma equation were treated with the Heinrich upwinding technique. The time integration was performed using an explicit two-step Lax-Wendroff procedure. The system of algebraic equations were solved with a fully-packed Gauss-Seidel iteration scheme. A value of 2/3 for the upwinding parameter was found to provide the best compromise between dispersion of the pulse, and computer storage requirements. The savings in computer memory results in increased execution speed for the algorithm. Also, it is shown that the numerical scheme does not permit spurious pulse reflections from the edges of the mesh. Results for several test cases are presented. Comparisons are given which show favorable agreement for the finite element technique with other solution relationships.

This paper is concerned with scattering of time-harmonic waves by compact inhomogeneities in an elastic solid. In the calculation procedure a boundary integral equation is solved numerically by the boundary element method (BEM). An alternative to the usual boundary element method is employed. The alternative approach is applicable to cavities or fixed rigid bodies of general shape located in linearly elastic, isotropic, homogeneous solids, but the specific results reported herein are for spherical cavities. The alternative approach eliminates the cumbersome singularities associated with the usual approach to BEM, and it also eliminates the problems encountered at the so called fictitious eigenfrequencies.

The deformation of an initially spherical capsule, freely suspended in simple shear flow, can be computed analytically in the limit of small deformations [D. Barthes-Biesel, J. M. Rallison, The Time-Dependent Deformation of a Capsule Freely Suspended in a Linear Shear Flow, J. Fluid Mech. 113 (1981) 251-267]. Those analytic approximations are used to study the influence of the mesh tessellation method, the spatial resolution, and the discrete delta function of the immersed boundary method on the numerical results obtained by a coupled immersed boundary lattice Boltzmann finite element method. For the description of the capsule membrane, a finite element method and the Skalak constitutive model [R. Skalak et al., Strain Energy Function of Red Blood Cell Membranes, Biophys. J. 13 (1973) 245-264] have been employed. Our primary goal is the investigation of the presented model for small resolutions to provide a sound basis for efficient but accurate simulations of multiple deformable particles immersed in a fluid. We come to the conclusion that details of the membrane mesh, as tessellation method and resolution, play only a minor role. The hydrodynamic resolution, i.e., the width of the discrete delta function, can significantly influence the accuracy of the simulations. The discretization of the delta function introduces an artificial length scale, which effectively changes the radius and the deformability of the capsule. We discuss possibilities of reducing the computing time of simulations of deformable objects immersed in a fluid while maintaining high accuracy.

The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach employs a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach.

In this paper we propose and analyse a hybrid numerical-asymptotic boundary element method for the solution of problems of high frequency acoustic scattering by a class of sound-soft nonconvex polygons. The approximation space is enriched with carefully chosen oscillatory basis functions; these are selected via a study of the high frequency asymptotic behaviour of the solution. We demonstrate via a rigorous error analysis, supported by numerical examples, that to achieve any desired accuracy it is sufficient for the number of degrees of freedom to grow only in proportion to the logarithm of the frequency as the frequency increases, in contrast to the at least linear growth required by conventional methods. This appears to be the first such numerical analysis result for any problem of scattering by a nonconvex obstacle. Our analysis is based on new frequency-explicit bounds on the normal derivative of the solution on the boundary and on its analytic continuation into the complex plane.

We consider linear acoustic propagation at a fixed frequency in a subsonic convective flow around a scattering object, under the assumption that the flow is uniform far away from the object. Using the Prandtl--Glauert transformation, the convected Helmholtz equation yields the classical Helmholtz equation in the exterior domain where the flow is uniform. We then derive two coupled methods to solve the problem approximately using the finite element method in the interior domain around the scattering object and the boundary element method on the coupling surface with the exterior domain. The first one admits infinitely many solutions at resonant frequencies. The second one is based on the combined field integral equations method, and is well-posed at all frequencies. We perform the analysis of the two formulations and present numerical results illustrating the advantages of the second formulation.

In this paper we present numerical modeling results for endcap and linear ion traps, used for experiments at the National Physical Laboratory in the UK and Innsbruck University respectively. The secular frequencies for Strontium-88 and Calcium-40 ions were calculated from ion trajectories, simulated using boundary-element and finite-difference numerical methods. The results were compared against experimental measurements. Both numerical methods showed high accuracy with boundary-element method being more accurate. Such simulations can be useful tools for designing new traps and trap arrays. They can also be used for obtaining precise trapping parameters for desired ion control when no analytical approach is possible as well as for investigating the ion heating rates due to thermal electronic noise.

An axisymmetric boundary element flow algorithm is coupled with a finite element structural analyzer to perform interactive calculations of the growth and subsequent collapse of an explosion bubble near a submerged compliant structure. The validity of the program is established through direct comparisons with published experimental data. A parametric study of the interaction between a growing and collapsing bubble and a spherical shell is presented. The results show that if the stiffness of the shell is sufficiently low, then the mass of the shell is a critical parameter in the collapse problem. If the mass of the structure is high, a reentrant jet forms and is then directed towards the shell. As the mass of the spherical shell is decreased, the collapse becomes spherical with no jet formation. At the lowest structural mass for which calculations are performed, a jet directed away from the structure begins to form. The ratio of the depth of submergence to bubble maximum radius was also found to be a critical parameter in the collapse problem. When this ratio is large (greater than 100), the collapse is driven by interaction forces. However, for shallow submergence, buoyancy effects become more important than interaction forces. Fluid-Structure Interaction, Boundary Element, Fluid Loading, Bubble Collapse, Numerical Prediction Method, Whipping, Finite Element, Cavitation.

Composite materials are involving in engineering applications at a growing speed, due to their stiffer, stronger and lighter properties. This growth requires fast and powerful numerical methods like Boundary Element Method (BEM), and Finite Element Method (FEM). BEM has become popular especially in the last decade due to its advantage of requiring less computation time for the same accuracy. The objective of this study is, by using Boundary Element Method, to examine different shapes of reinforcement elements under unit traction and unit displacement boundary conditions in transversal direction and perfect interfacial bonding. The stress variations along the interface of the matrix and reinforcing material, effective elastic modulus of composites were studied due to different shapes and different volume fractions of reinforcement elements. These calculations were made for both the internal Representative Volume Element (RVE), and boundary RVE, which are the internal and boundary cells of composite material respectively. Finally, using an appropriate failure criterion, the failures of different shapes were examined and also the effective elastic modulus variations of the shapes during the progress of the failure for both internal and boundary RVE were studied.

Composite materials are involving in engineering applications at a growing speed, due to their stiffer, stronger and lighter properties. This growth requires fast and powerful numerical methods like Boundary Element Method (BEM), and Finite Element Method (FEM). BEM has become popular especially in the last decade due to its advantage of requiring less computation time for the same accuracy. The objective of this study is, by using Boundary Element Method, to examine different shapes of reinforcement elements under unit traction and unit displacement boundary conditions in transversal direction and perfect interfacial bonding. The stress variations along the interface of the matrix and reinforcing material, effective elastic modulus of composites were studied due to different shapes and different volume fractions of reinforcement elements. These calculations were made for both the internal Representative Volume Element (RVE), and boundary RVE, which are the internal and boundary cells of composite material respectively. Finally, using an appropriate failure criterion, the failures of different shapes were examined and also the effective elastic modulus variations of the shapes during the progress of the failure for both internal and boundary RVE were studied.

Book Source: Digital Library of India Item 2015.228710 dc.contributor.author: Atul Kumar Agrawal dc.date.accessioned: 2015-07-10T15:51:14Z dc.date.available: 2015-07-10T15:51:14Z dc.date.digitalpublicationdate: 0000-00-00 dc.identifier.barcode: 5990010117631 dc.identifier.origpath: /rawdataupload/upload/0117/633 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/228710 dc.description.scanningcentre: IIIT, Allahabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 195 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher: Iit Kanpur dc.rights: Out_of_copyright dc.source.library: I I T Kanpur dc.subject.classification: Technology dc.subject.classification: Engineering. Technology In General dc.subject.classification: Mechanical Engineering In General. Nuclear Technology. Electrical Engineering. Machinery dc.title: A Study Of Free Surface Effects On Through Cracks Under Static And Dynamic Conditions Using Boundary Element Method

An isogeometric boundary element method for problems in elasticity is presented, which is based on an independent approximation for the geometry, traction and displacement field. This enables a flexible choice of refinement strategies, permits an efficient evaluation of geometry related information, a mixed collocation scheme which deals with discontinuous tractions along non-smooth boundaries and a significant reduction of the right hand side of the system of equations for common boundary conditions. All these benefits are achieved without any loss of accuracy compared to conventional isogeometric formulations. The system matrices are approximated by means of hierarchical matrices to reduce the computational complexity for large scale analysis. For the required geometrical bisection of the domain, a strategy for the evaluation of bounding boxes containing the supports of NURBS basis functions is presented. The versatility and accuracy of the proposed methodology is demonstrated by convergence studies showing optimal rates and real world examples in two and three dimensions.

In this contribution we develop a cut finite element method with boundary value correction of the type originally proposed by Bramble, Dupont, and Thomee. The cut finite element method is a fictitious domain method with Nitsche type enforcement of Dirichlet conditions together with stabilization of the elements at the boundary which is stable and enjoy optimal order approximation properties. A computational difficulty is, however, the geometric computations related to quadrature on the cut elements which must be accurate enough to achieve higher order approximation. With boundary value correction we may use only a piecewise linear approximation of the boundary, which is very convenient in a cut finite element method, and still obtain optimal order convergence. The boundary value correction is a modified Nitsche formulation involving a Taylor expansion in the normal direction compensating for the approximation of the boundary. Key to the analysis is a consistent stabilization term which enables us to prove stability of the method and a priori error estimates with explicit dependence on the meshsize and distance between the exact and approximate boundary.

In this contribution we develop a cut finite element method with boundary value correction of the type originally proposed by Bramble, Dupont, and Thomee. The cut finite element method is a fictitious domain method with Nitsche type enforcement of Dirichlet conditions together with stabilization of the elements at the boundary which is stable and enjoy optimal order approximation properties. A computational difficulty is, however, the geometric computations related to quadrature on the cut elements which must be accurate enough to achieve higher order approximation. With boundary value correction we may use only a piecewise linear approximation of the boundary, which is very convenient in a cut finite element method, and still obtain optimal order convergence. The boundary value correction is a modified Nitsche formulation involving a Taylor expansion in the normal direction compensating for the approximation of the boundary. Key to the analysis is a consistent stabilization term which enables us to prove stability of the method and a priori error estimates with explicit dependence on the meshsize and distance between the exact and approximate boundary.

We propose and analyse a hybrid numerical-asymptotic $hp$ boundary element method for time-harmonic scattering of an incident plane wave by an arbitrary collinear array of sound-soft two-dimensional screens. Our method uses an approximation space enriched with oscillatory basis functions, chosen to capture the high frequency asymptotics of the solution. We provide a rigorous frequency-explicit error analysis which proves that the method converges exponentially as the number of degrees of freedom $N$ increases, and that to achieve any desired accuracy it is sufficient to increase $N$ in proportion to the square of the logarithm of the frequency as the frequency increases (standard boundary element methods require $N$ to increase at least linearly with frequency to retain accuracy). Our numerical results suggest that fixed accuracy can in fact be achieved at arbitrarily high frequencies with a frequency-independent computational cost, when the oscillatory integrals required for implementation are computed using Filon quadrature. We also show how our method can be applied to the complementary "breakwater" problem of propagation through an aperture in an infinite sound-hard screen.

A quadrature method for second-order, curved triangular elements in the Boundary Element Method (BEM) is presented, based on a polar coordinate transformation, combined with elementary geometric operations. The numerical performance of the method is presented using results from solution of the Laplace equation on a cat's eye geometry which show an error of order $P^{-1.6}$, where $P$ is the number of elements.

This paper describes how Large Deformation Diffeomorphic Metric Mapping (LDDMM) can be coupled with a Fast Multipole (FM) Boundary Element Method (BEM) to investigate the relationship between morphological changes in the head, torso, and outer ears and their acoustic filtering (described by Head Related Transfer Functions, HRTFs). The LDDMM technique provides the ability to study and implement morphological changes in ear, head and torso shapes. The FM-BEM technique provides numerical simulations of the acoustic properties of an individual's head, torso, and outer ears. This paper describes the first application of LDDMM to the study of the relationship between a listener's morphology and a listener's HRTFs. To demonstrate some of the new capabilities provided by the coupling of these powerful tools, we examine the classical question of what it means to ``listen through another individual's outer ears.'' This work utilizes the data provided by the Sydney York Morphological and Acoustic Recordings of Ears (SYMARE) database.

Book Source: Digital Library of India Item 2015.199190 dc.contributor.author: Venkatesh, Jakka dc.date.accessioned: 2015-07-08T13:07:44Z dc.date.available: 2015-07-08T13:07:44Z dc.date.digitalpublicationdate: 2005-08-27 dc.identifier.barcode: 5990010101587 dc.identifier.origpath: /rawdataupload/upload/0101/589 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/199190 dc.description.scannerno: 14 dc.description.scanningcentre: IIIT, Allahabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 169 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher: Indian Institute Of Technology Kanpur dc.rights: Out_of_copyright dc.source.library: Indian Institute Of Technology Kanpur dc.subject.classification: Technology dc.subject.classification: Engineering. Technology In General dc.title: Shape Optimization Using Intrinsic Geometry And Boundary Element Method

Book Source: Digital Library of India Item 2015.225110 dc.contributor.author: Ankit Kumar Garg dc.date.accessioned: 2015-07-10T15:28:39Z dc.date.available: 2015-07-10T15:28:39Z dc.date.digitalpublicationdate: 2005-09-08 dc.identifier.barcode: 5990010120191 dc.identifier.origpath: /rawdataupload/upload/0120/193 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/225110 dc.description.scannerno: 15 dc.description.scanningcentre: IIIT, Allahabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 96 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher: Indian Institute Of Technology Kanpur dc.rights: Out_of_copyright dc.source.library: Indian Institute Of Technology Kanpur dc.subject.classification: Technology dc.subject.classification: Engineering. Technology In General dc.subject.classification: Mechanical Engineering In General. Nuclear Technology. Electrical Engineering. Machinery dc.title: Stress Migration Failure Analysis Of Aluminium Line Of A Multilavel Printed Circuit Board Using Boundary Element Method

Book Source: Digital Library of India Item 2015.225110 dc.contributor.author: Ankit Kumar Garg dc.date.accessioned: 2015-07-10T15:28:39Z dc.date.available: 2015-07-10T15:28:39Z dc.date.digitalpublicationdate: 2005-09-08 dc.identifier.barcode: 5990010120191 dc.identifier.origpath: /rawdataupload/upload/0120/193 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/225110 dc.description.scannerno: 15 dc.description.scanningcentre: IIIT, Allahabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 96 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher: Indian Institute Of Technology Kanpur dc.rights: Out_of_copyright dc.source.library: Indian Institute Of Technology Kanpur dc.subject.classification: Technology dc.subject.classification: Engineering. Technology In General dc.subject.classification: Mechanical Engineering In General. Nuclear Technology. Electrical Engineering. Machinery dc.title: Stress Migration Failure Analysis Of Aluminium Line Of A Multilavel Printed Circuit Board Using Boundary Element Method

As model problem we consider the prototype for flow and transport of a concentration in porous media in an interior domain and couple it with a diffusion process in the corresponding unbounded exterior domain. To solve the problem we develop a new non-symmetric coupling between the vertex-centered finite volume and boundary element method. This discretization provides naturally conservation of local fluxes and with an upwind option also stability in the convection dominated case. We aim to provide a first rigorous analysis of the system for different model parameters; stability, convergence, and a~priori estimates. This includes the use of an implicit stabilization, known from the finite element and boundary element method coupling. Some numerical experiments conclude the work and confirm the theoretical results.

As model problem we consider the prototype for flow and transport of a concentration in porous media in an interior domain and couple it with a diffusion process in the corresponding unbounded exterior domain. To solve the problem we develop a new non-symmetric coupling between the vertex-centered finite volume and boundary element method. This discretization provides naturally conservation of local fluxes and with an upwind option also stability in the convection dominated case. We aim to provide a first rigorous analysis of the system for different model parameters; stability, convergence, and a~priori estimates. This includes the use of an implicit stabilization, known from the finite element and boundary element method coupling. Some numerical experiments conclude the work and confirm the theoretical results.

Many boundary element integral equation kernels are based on the Green's functions of the Laplace and Helmholtz equations in three dimensions. These include, for example, the Laplace, Helmholtz, elasticity, Stokes, and Maxwell's equations. Integral equation formulations lead to more compact, but dense linear systems. These dense systems are often solved iteratively via Krylov subspace methods, which may be accelerated via the fast multipole method. There are advantages to Galerkin formulations for such integral equations, as they treat problems associated with kernel singularity, and lead to symmetric and better conditioned matrices. However, the Galerkin method requires each entry in the system matrix to be created via the computation of a double surface integral over one or more pairs of triangles. There are a number of semi-analytical methods to treat these integrals, which all have some issues, and are discussed in this paper. We present novel methods to compute all the integrals that arise in Galerkin formulations involving kernels based on the Laplace and Helmholtz Green's functions to any specified accuracy. Integrals involving completely geometrically separated triangles are non-singular and are computed using a technique based on spherical harmonics and multipole expansions and translations, which results in the integration of polynomial functions over the triangles. Integrals involving cases where the triangles have common vertices, edges, or are coincident are treated via scaling and symmetry arguments, combined with automatic recursive geometric decomposition of the integrals. Example results are presented, and the developed software is available as open source.

Composite materials are involving in engineering applications at a growing speed, due to their stiffer, stronger and lighter properties. This growth requires fast and powerful numerical methods like Boundary Element Method (BEM), and Finite Element Method (FEM). BEM has become popular especially in the last decade due to its advantage of requiring less computation time for the same accuracy. The objective of this study is, by using Boundary Element Method, to examine different shapes of reinforcement elements under unit traction and unit displacement boundary conditions in transversal direction and perfect interfacial bonding. The stress variations along the interface of the matrix and reinforcing material, effective elastic modulus of composites were studied due to different shapes and different volume fractions of reinforcement elements. These calculations were made for both the internal Representative Volume Element (RVE), and boundary RVE, which are the internal and boundary cells of composite material respectively. Finally, using an appropriate failure criterion, the failures of different shapes were examined and also the effective elastic modulus variations of the shapes during the progress of the failure for both internal and boundary RVE were studied.