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This paper applies the technique of the h-p version to the boundary element method for boundary value problems on non-smooth, plane domains with piecewise analytic boundary and data. The exponential rate of convergence of the boundary element Galerkin solution is proven when a geometric mesh refinement towards the vertices is used. (KR)

This paper applies the technique of the h-p version to the boundary element method for boundary value problems on non-smooth, plane domains with piecewise analytic boundary and data. The exponential rate of convergence of the boundary element Galerkin solution is proven when a geometric mesh refinement towards the vertices is used. (KR)

This paper applies the technique of the h-p version to the boundary element method for boundary value problems on non-smooth, plane domains with piecewise analytic boundary and data. The exponential rate of convergence of the boundary element Galerkin solution is proven when a geometric mesh refinement towards the vertices is used. (KR)

This paper applies the technique of the h-p version to the boundary element method for boundary value problems on non-smooth, plane domains with piecewise analytic boundary and data. The exponential rate of convergence of the boundary element Galerkin solution is proven when a geometric mesh refinement towards the vertices is used. (KR)

This paper presents a new approach to the analysis of finite element methods based on C-finite elements for the approximate solution of 2nd order boundary value problems in which error estimates are derived directly in terms of two mesh dependent norms that are closely related to the L2 norm and to the 2nd order Sobolev norm, respectively, and in which there is no assumption of quasi-uniformity on the mesh family. This is in contrast to the usual analysis in which error estimates are first derived in the 1st order Sobolev norm and subsequently are derived in the L2 norm and in the 2nd order Sobolev norm - the 2nd order Sobolev norm estimates being obtained under the assumption that the functions in the underlying approximating subspaces lie in the 2nd order Sobolev space and that the mesh family is quasi-uniform. (Author)

Recent progress in the simulation of Casimir forces between various objects has allowed traditional computational electromagnetic solvers to be used to find Casimir forces in arbitrary three-dimensional objects. The underlying theory to these approaches requires knowledge and manipulation of quantum field theory and statistical physics. We present a calculation of the Casimir force using the method of moments via the argument principle. This simplified derivation allows greater freedom in the moment matrix where the argument principle can be used to calculate Casimir forces for arbitrary geometries and materials with the use of various computational electromagnetic techniques.

Recent progress in the simulation of Casimir forces between various objects has allowed traditional computational electromagnetic solvers to be used to find Casimir forces in arbitrary three-dimensional objects. The underlying theory to these approaches requires knowledge and manipulation of quantum field theory and statistical physics. We present a calculation of the Casimir force using the method of moments via the argument principle. This simplified derivation allows greater freedom in the moment matrix where the argument principle can be used to calculate Casimir forces for arbitrary geometries and materials with the use of various computational electromagnetic techniques.

This study investigates the coupling of the finite and boundary element methods in elastostatics where each method is used to model a different portion of the domain. The principal interest is in applying a boundary element method (BEM) to model the infinite domain (assumed to be isotropic linear elastic) while using the finite element method (FEM) to model regions with more complex constitutive relations. The approach taken in this study, referred to as a FEM-hosted coupling, treats each BEM subdomain as a single finite element. Two derivations for an IBEM stiffness matrix are given; the first is a physically intuitive direct derivation while the second is the corresponding variational derivation. Though the emphasis is on the IBEM, the DBEM is also addressed. The inherent incompatibility between the BEM and FEM methods is discussed and explained in terms of the shape function fallacy.

A coupled boundary element (BEM)-finite element (FEM) approach is presented to accurately model structure-acoustic interaction systems. The boundary element method is first applied to interior, two and three-dimensional acoustic domains with complex geometry configurations. Boundary element results are very accurate when compared with limited exact solutions. Structure-interaction problems are then analyzed with the coupled FEM-BEM method, where the finite element method models the structure and the boundary element method models the interior acoustic domain. The coupled analysis is compared with exact and experimental results for a simplistic model. Composite panels are analyzed and compared with isotropic results. The coupled method is then extended for random excitation. Random excitation results are compared with uncoupled results for isotropic and composite panels.

Analytical and experimental validation of methods to predict structural vibration and radiated noise are presented. A rectangular box excited by a mechanical shaker was used as a vibrating structure. Combined finite element method (FEM) and boundary element method (BEM) models of the apparatus were used to predict the noise radiated from the box. The FEM was used to predict the vibration, and the surface vibration was used as input to the BEM to predict the sound intensity and sound power. Vibration predicted by the FEM model was validated by experimental modal analysis. Noise predicted by the BEM was validated by sound intensity measurements. Three types of results are presented for the total radiated sound power: (1) sound power predicted by the BEM modeling using vibration data measured on the surface of the box; (2) sound power predicted by the FEM/BEM model; and (3) sound power measured by a sound intensity scan. The sound power predicted from the BEM model using measured vibration data yields an excellent prediction of radiated noise. The sound power predicted by the combined FEM/BEM model also gives a good prediction of radiated noise except for a shift of the natural frequencies that are due to limitations in the FEM model.

We propose time-domain boundary integral and coupled boundary integral and variational formulations for acoustic scattering by linearly elastic obstacles. Well posedness along with stability and error bounds with explicit time dependence are established. Full discretization is achieved coupling boundary and finite elements; Convolution Quadrature is used for time evolution in the pure BIE formulation and combined with time stepping in the coupled BEM/FEM scenario. Second order convergence in time is proven for BDF2-CQ and numerical experiments are provided for both BDF2 and Trapezoidal Rule CQ showing second order behavior for the latter as well.

Experimental validation of methods to predict radiated noise is presented. A combined finite element and boundary element model was used to predict the vibration and noise of a rectangular box excited by a mechanical shaker. The predicted noise was compared to sound power measured by the acoustic intensity method. Inaccuracies in the finite element model shifted the resonance frequencies by about 5 percent. The predicted and measured sound power levels agree within about 2.5 dB. In a second experiment, measured vibration data was used with a boundary element model to predict noise radiation from the top of an operating gearbox. The predicted and measured sound power for the gearbox agree within about 3 dB.

The primary purpose of this paper is to compare the accuracy and performance of two numerical approaches to solving systems of partial differential equations. These equations are posed on adjoining domains sharing boundary conditions on a common boundary interface in the important case when the meshes used on the two domains are non-matching across the interface. The first widely used approach is based on a finite volume method employing ad hoc projections to relate approximations on the two domains across the interface. The second approach uses the mathematically-founded mortar mixed finite element method. To quantify the performance, we use a goal-oriented a-posteriori error estimate that quantifies various aspects of discretization error to the overall error. While the performance difference may be not a surprise in some cases, we believe that there is a perception in part of the scientific community concerned with multiphysics systems that if the solution is smooth near the interface, then there is little effect from varying the coupling technique. We find that, on the contrary, the error associated with ad hoc coupling approaches may be large in practical situations. Moreover, we also show that mortar methods can be used with black box component solves, thus permitting an efficient and practical implementation also within legacy codes.

The primary purpose of this paper is to compare the accuracy and performance of two numerical approaches to solving systems of partial differential equations. These equations are posed on adjoining domains sharing boundary conditions on a common boundary interface in the important case when the meshes used on the two domains are non-matching across the interface. The first widely used approach is based on a finite volume method employing ad hoc projections to relate approximations on the two domains across the interface. The second approach uses the mathematically-founded mortar mixed finite element method. To quantify the performance, we use a goal-oriented a-posteriori error estimate that quantifies various aspects of discretization error to the overall error. While the performance difference may be not a surprise in some cases, we believe that there is a perception in part of the scientific community concerned with multiphysics systems that if the solution is smooth near the interface, then there is little effect from varying the coupling technique. We find that, on the contrary, the error associated with ad hoc coupling approaches may be large in practical situations. Moreover, we also show that mortar methods can be used with black box component solves, thus permitting an efficient and practical implementation also within legacy codes.

The primary purpose of this paper is to compare the accuracy and performance of two numerical approaches to solving systems of partial differential equations. These equations are posed on adjoining domains sharing boundary conditions on a common boundary interface in the important case when the meshes used on the two domains are non-matching across the interface. The first widely used approach is based on a finite volume method employing ad hoc projections to relate approximations on the two domains across the interface. The second approach uses the mathematically-founded mortar mixed finite element method. To quantify the performance, we use a goal-oriented a-posteriori error estimate that quantifies various aspects of discretization error to the overall error. While the performance difference may be not a surprise in some cases, we believe that there is a perception in part of the scientific community concerned with multiphysics systems that if the solution is smooth near the interface, then there is little effect from varying the coupling technique. We find that, on the contrary, the error associated with ad hoc coupling approaches may be large in practical situations. Moreover, we also show that mortar methods can be used with black box component solves, thus permitting an efficient and practical implementation also within legacy codes.

The primary purpose of this paper is to compare the accuracy and performance of two numerical approaches to solving systems of partial differential equations. These equations are posed on adjoining domains sharing boundary conditions on a common boundary interface in the important case when the meshes used on the two domains are non-matching across the interface. The first widely used approach is based on a finite volume method employing ad hoc projections to relate approximations on the two domains across the interface. The second approach uses the mathematically-founded mortar mixed finite element method. To quantify the performance, we use a goal-oriented a-posteriori error estimate that quantifies various aspects of discretization error to the overall error. While the performance difference may be not a surprise in some cases, we believe that there is a perception in part of the scientific community concerned with multiphysics systems that if the solution is smooth near the interface, then there is little effect from varying the coupling technique. We find that, on the contrary, the error associated with ad hoc coupling approaches may be large in practical situations. Moreover, we also show that mortar methods can be used with black box component solves, thus permitting an efficient and practical implementation also within legacy codes.

We consider the Shallow Water equations in the supercritical and subcritical cases in one space variable,posed in a finite spatial interval with characteristic boundary conditions at the endpoints, which, as is well known, are transparent,i.e. allow outgoing waves to exit without generating spurious reflected waves. Assuming that the resulting initial-boundary-value problems have smooth solutions,we approximate them in space using standard Galerkin-finite element methods and prove L^2 error estimates for the semidiscrete problems on quasiuniform meshes.We discretize the problems in the temporal variable using an explicit,fourth-order accurate Runge-Kutta scheme and check, by means of numerical experiment, that the resulting fully discrete schemes have excellent absorption properties.

We consider the Shallow Water equations in the supercritical and subcritical cases in one space variable,posed in a finite spatial interval with characteristic boundary conditions at the endpoints, which, as is well known, are transparent,i.e. allow outgoing waves to exit without generating spurious reflected waves. Assuming that the resulting initial-boundary-value problems have smooth solutions,we approximate them in space using standard Galerkin-finite element methods and prove L^2 error estimates for the semidiscrete problems on quasiuniform meshes.We discretize the problems in the temporal variable using an explicit,fourth-order accurate Runge-Kutta scheme and check, by means of numerical experiment, that the resulting fully discrete schemes have excellent absorption properties.

We consider the Shallow Water equations in the supercritical and subcritical cases in one space variable,posed in a finite spatial interval with characteristic boundary conditions at the endpoints, which, as is well known, are transparent,i.e. allow outgoing waves to exit without generating spurious reflected waves. Assuming that the resulting initial-boundary-value problems have smooth solutions,we approximate them in space using standard Galerkin-finite element methods and prove L^2 error estimates for the semidiscrete problems on quasiuniform meshes.We discretize the problems in the temporal variable using an explicit,fourth-order accurate Runge-Kutta scheme and check, by means of numerical experiment, that the resulting fully discrete schemes have excellent absorption properties.

Book Source: Digital Library of India Item 2015.193316 dc.contributor.author: Amiya Kumar Pani dc.date.accessioned: 2015-07-08T02:30:55Z dc.date.available: 2015-07-08T02:30:55Z dc.date.digitalpublicationdate: 2005-08-27 dc.identifier.barcode: 1990010086728 dc.identifier.origpath: /rawdataupload/upload/0086/728 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/193316 dc.description.scannerno: 14 dc.description.scanningcentre: IIIT, Allahabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 180 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: Finite Element Methods For Nonlinear Free Boundary Problems

This research report is presented in three parts. In the first part, acoustical analyses were performed on modes of vibration of the housing of a transmission of a gear test rig developed by NASA. The modes of vibration of the transmission housing were measured using experimental modal analysis. The boundary element method (BEM) was used to calculate the sound pressure and sound intensity on the surface of the housing and the radiation efficiency of each mode. The radiation efficiency of each of the transmission housing modes was then compared to theoretical results for a finite baffled plate. In the second part, analytical and experimental validation of methods to predict structural vibration and radiated noise are presented. A rectangular box excited by a mechanical shaker was used as a vibrating structure. Combined finite element method (FEM) and boundary element method (BEM) models of the apparatus were used to predict the noise level radiated from the box. The FEM was used to predict the vibration, while the BEM was used to predict the sound intensity and total radiated sound power using surface vibration as the input data. Vibration predicted by the FEM model was validated by experimental modal analysis; noise predicted by the BEM was validated by measurements of sound intensity. Three types of results are presented for the total radiated sound power: sound power predicted by the BEM model using vibration data measured on the surface of the box; sound power predicted by the FEM/BEM model; and sound power measured by an acoustic intensity scan. In the third part, the structure used in part two was modified. A rib was attached to the top plate of the structure. The FEM and BEM were then used to predict structural vibration and radiated noise respectively. The predicted vibration and radiated noise were then validated through experimentation.

An alternative method for performing singular boundary element integrals for applications in linear acoustics is discussed. The method separates the integral of the characteristic solution into a singular and nonsingular part. The singular portion is integrated with a combination of analytic and numerical techniques while the nonsingular portion is integrated with standard Gaussian quadrature. The method may be generalized to many types of subparametric elements. The integrals over elements containing the root node are considered, and the characteristic solution for linear acoustic problems are examined. The method may be generalized to most characteristic solutions.

The comparative computational efficiencies of the finite element (FEM), boundary element (BEM), and hybrid boundary element-finite element (HVFEM) analysis techniques are evaluated for representative bounded domain interior and unbounded domain exterior problems in elastostatics. Computational efficiency is carefully defined in this study as the computer time required to attain a specified level of solution accuracy. The study found the FEM superior to the BEM for the interior problem, while the reverse was true for the exterior problem. The hybrid analysis technique was found to be comparable or superior to both the FEM and BEM for both the interior and exterior problems.

Boundary element algorithms for the solution of steady-state and transient heat conduction are presented. The algorithms are designed for efficient coupling with computational fluid dynamic discretizations and feature piecewise linear elements with offset nodal points. The steady-state algorithm employs the fundamental solution approach; the integration kernels are computed analytically based on linear shape functions, linear elements, and variably offset nodal points. The analytic expressions for both singular and nonsingular integrands are presented. The transient algorithm employs the transient fundamental solution; the temporal integration is performed analytically and the nonsingular spatial integration is performed numerically using Gaussian quadrature. A series solution to the integration is derived for the instance of a singular integrand. The boundary-only character of the algorithm is maintained by integrating the influence coefficients from initial time. Numerical results are compared to analytical solutions to verify the current boundary element algorithms. The steady-state and transient algorithms are numerically shown to be second-order accurate in space and time, respectively.

Boundary element algorithms for the solution of steady-state and transient heat conduction are presented. The algorithms are designed for efficient coupling with computational fluid dynamic discretizations and feature piecewise linear elements with offset nodal points. The steady-state algorithm employs the fundamental solution approach; the integration kernels are computed analytically based on linear shape functions, linear elements, and variably offset nodal points. The analytic expressions for both singular and nonsingular integrands are presented. The transient algorithm employs the transient fundamental solution; the temporal integration is performed analytically and the nonsingular spatial integration is performed numerically using Gaussian quadrature. A series solution to the integration is derived for the instance of a singular integrand. The boundary-only character of the algorithm is maintained by integrating the influence coefficients from initial time. Numerical results are compared to analytical solutions to verify the current boundary element algorithms. The steady-state and transient algorithms are numerically shown to be second-order accurate in space and time, respectively.

This paper reviews the state of the art and discusses very recent mathematical developments in the field of adaptive boundary element methods. This includes an overview of available a posteriori error estimates as well as a state-of-the-art formulation of convergence and quasi-optimality of adaptive mesh-refining algorithms.

This study investigates the time domain coupling of the boundary and finite element methods for elastodynamics. The study is motivated by the need for a 'silent boundary' in nonlinear problems with infinite domains. Of the boundary element methods (BEMs) considered, formulations based on the Stokes solution appear to be the best suited. The theoretical and numerical bases for the indirect and direct BEMs using the Stokes solution are presented. The integral equation statements of the boundary-initial value problem included a convolution of the time variable and thus appear to be computationally intense. A coupling algorithm which treats the BEM region as a nonlinear boundary condition to the finite element region is presented. The potential of the coupled approach might be realized by exploiting special properties of Stoke's solution and designing the algorithm to use the advances in computer hardware (e.g. parallel processing).

Until quite recently, few effective numerical solution techniques were known for solving two-point boundary value problems for the equation -d/dx(p(x)du/dx) + qu = f, 0 x 1, p(0) = 0. This dissertation analyzes several new finite element methods for approximating the solution of this problem, and presents new analysis for some known methods.

Until quite recently, few effective numerical solution techniques were known for solving two-point boundary value problems for the equation -d/dx(p(x)du/dx) + qu = f, 0 x 1, p(0) = 0. This dissertation analyzes several new finite element methods for approximating the solution of this problem, and presents new analysis for some known methods.

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We consider the Galerkin boundary element method (BEM) for weakly-singular integral equations of the first-kind in 2D. We analyze some residual-type a posteriori error estimator which provides a lower as well as an upper bound for the unknown Galerkin BEM error. The required assumptions are weak and allow for piecewise smooth parametrizations of the boundary, local mesh-refinement, and related standard piecewise polynomials as well as NURBS. In particular, our analysis gives a first contribution to adaptive BEM in the frame of isogeometric analysis (IGABEM), for which we formulate an adaptive algorithm which steers the local mesh-refinement and the multiplicity of the knots. Numerical experiments underline the theoretical findings and show that the proposed adaptive strategy leads to optimal convergence.

We describe some recent advances in the numerical solution of acoustic scattering problems. A major focus of the paper is the efficient solution of high frequency scattering problems via hybrid numerical-asymptotic boundary element methods. We also make connections to the unified transform method due to A.S. Fokas and co-authors, analysing particular instances of this method, proposed by J.A. DeSanto and co-authors, for problems of acoustic scattering by diffraction gratings.

We introduce a framework for the design of finite element methods for two-dimensional moving boundary problems with prescribed boundary evolution that have arbitrarily high order of accuracy, both in space and in time. At the core of our approach is the use of a universal mesh: a stationary background mesh containing the domain of interest for all times that adapts to the geometry of the immersed domain by adjusting a small number of mesh elements in the neighborhood of the moving boundary. The resulting method maintains an exact representation of the (prescribed) moving boundary at the discrete level, or an approximation of the appropriate order, yet is immune to large distortions of the mesh under large deformations of the domain. The framework is general, making it possible to achieve any desired order of accuracy in space and time by selecting a preferred and suitable finite-element space on the universal mesh for the problem at hand, and a preferred and suitable time integrator for ordinary differential equations. We illustrate our approach by constructing a particular class of methods, and apply them to a prescribed-boundary variant of the Stefan problem. We present numerical evidence for the order of accuracy of our schemes in one and two dimensions.

We introduce a framework for the design of finite element methods for two-dimensional moving boundary problems with prescribed boundary evolution that have arbitrarily high order of accuracy, both in space and in time. At the core of our approach is the use of a universal mesh: a stationary background mesh containing the domain of interest for all times that adapts to the geometry of the immersed domain by adjusting a small number of mesh elements in the neighborhood of the moving boundary. The resulting method maintains an exact representation of the (prescribed) moving boundary at the discrete level, or an approximation of the appropriate order, yet is immune to large distortions of the mesh under large deformations of the domain. The framework is general, making it possible to achieve any desired order of accuracy in space and time by selecting a preferred and suitable finite-element space on the universal mesh for the problem at hand, and a preferred and suitable time integrator for ordinary differential equations. We illustrate our approach by constructing a particular class of methods, and apply them to a prescribed-boundary variant of the Stefan problem. We present numerical evidence for the order of accuracy of our schemes in one and two dimensions.

Analytical and experimental validation of methods to predict structural vibration and radiated noise is presented in this paper. A rectangular box excited by a mechanical shaker was used as a vibrating structure. Combined finite element method (FEM) and boundary element method (BEM) models of the apparatus were used to predict the noise radiated from the box. The FEM was used to predict the vibration, and the surface vibration was used as input to the BEM to predict the sound intensity and sound power. Vibration predicted by the FEM model was validated by experimental modal analysis. Noise predicted by the BEM was validated by sound intensity measurements. Three types of results are presented for the total radiated sound power: (1) sound power predicted by the BEM model using vibration data measured on the surface of the box, (2) sound power predicted by the FEM/BEM model, and (3) sound power measured by a sound intensity scan. The sound power predicted from the BEM model using measured vibration data yields an excellent prediction of radiated noise. The sound power predicted by the combined FEM/BEM model also gives a good prediction of radiated noise except for a shift of the natural frequencies that are due to limitations in the FEM model. Acoustic intensity, Noise, Vibration, Boundary clement, Finite element.

This research report is presented in three parts. In the first part, acoustical analyses were performed on modes of vibration of the housing of a transmission of a gear test rig developed by NASA. The modes of vibration of the transmission housing were measured using experimental modal analysis. The boundary element method (BEM) was used to calculate the sound pressure and sound intensity on the surface of the housing, and the radiation efficiency of each mode. The radiation efficiency of each of the transmission housing modes was then compared to theoretical results for a finite baffled plate. In the second part, analytical and experimental validation of methods to predict structural vibration and radiated noise are presented. A rectangular box excited by a mechanical shaker was used as a vibrating structure. Combined finite element method (FEM) and boundary element method (BEM) models of the apparatus were used to predict the noise level radiated from the box. The FEM was used to predict the vibration, while the BEM was used to predict the sound intensity and total radiated sound power using surface vibration as the input data. Vibration predicted by the FEM model was validated by experimental modal analysis, noise predicted by the BEM was validated by measurements of sound intensity. Three types of results are presented for the total radiated sound power: (1) sound power predicted by the BEM model using vibration data measured on the surface of the box: (2) sound power predicted by the FEM/BEM model; and (3) sound power measured by an acoustic intensity scan. In the third part, the structure used in part two was modified. A rib was attached to the top plate of the structure. The FEM and BEM were then used to predict structural vibration and radiated noise respectively. (MM)

This research report is presented in three parts. In the first part, acoustical analyses were performed on modes of vibration of the housing of a transmission of a gear test rig developed by NASA. The modes of vibration of the transmission housing were measured using experimental modal analysis. The boundary element method (BEM) was used to calculate the sound pressure and sound intensity on the surface of the housing, and the radiation efficiency of each mode. The radiation efficiency of each of the transmission housing modes was then compared to theoretical results for a finite baffled plate. In the second part, analytical and experimental validation of methods to predict structural vibration and radiated noise are presented. A rectangular box excited by a mechanical shaker was used as a vibrating structure. Combined finite element method (FEM) and boundary element method (BEM) models of the apparatus were used to predict the noise level radiated from the box. The FEM was used to predict the vibration, while the BEM was used to predict the sound intensity and total radiated sound power using surface vibration as the input data. Vibration predicted by the FEM model was validated by experimental modal analysis, noise predicted by the BEM was validated by measurements of sound intensity. Three types of results are presented for the total radiated sound power: (1) sound power predicted by the BEM model using vibration data measured on the surface of the box: (2) sound power predicted by the FEM/BEM model; and (3) sound power measured by an acoustic intensity scan. In the third part, the structure used in part two was modified. A rib was attached to the top plate of the structure. The FEM and BEM were then used to predict structural vibration and radiated noise respectively. (MM)

This research report is presented in three parts. In the first part, acoustical analyses were performed on modes of vibration of the housing of a transmission of a gear test rig developed by NASA. The modes of vibration of the transmission housing were measured using experimental modal analysis. The boundary element method (BEM) was used to calculate the sound pressure and sound intensity on the surface of the housing, and the radiation efficiency of each mode. The radiation efficiency of each of the transmission housing modes was then compared to theoretical results for a finite baffled plate. In the second part, analytical and experimental validation of methods to predict structural vibration and radiated noise are presented. A rectangular box excited by a mechanical shaker was used as a vibrating structure. Combined finite element method (FEM) and boundary element method (BEM) models of the apparatus were used to predict the noise level radiated from the box. The FEM was used to predict the vibration, while the BEM was used to predict the sound intensity and total radiated sound power using surface vibration as the input data. Vibration predicted by the FEM model was validated by experimental modal analysis, noise predicted by the BEM was validated by measurements of sound intensity. Three types of results are presented for the total radiated sound power: (1) sound power predicted by the BEM model using vibration data measured on the surface of the box: (2) sound power predicted by the FEM/BEM model; and (3) sound power measured by an acoustic intensity scan. In the third part, the structure used in part two was modified. A rib was attached to the top plate of the structure. The FEM and BEM were then used to predict structural vibration and radiated noise respectively. (MM)

The comparative computational efficiencies of the finite element (FEM), boundary element (BEM), and hybrid boundary element-finite element (HBFEM) analysis techniques are evaluated for representative bounded domain interior and unbounded domain exterior problems in elastostatics. Computational efficiency is carefully defined in this study as the computer time required to attain a specified level of solution accuracy. The study found the FEM superior to the BEM for the interior problem, while the reverse was true for the exterior problem. The hybrid analysis technique was found to be comparable or superior to both the FEM and BEM for both the interior and exterior problems.

We derive and discuss a posteriori error estimators for Galerkin and collocation IGA boundary element methods for weakly-singular integral equations of the first-kind in 2D. While recent own work considered the Faermann residual error estimator for Galerkin IGA boundary element methods, the present work focuses more on collocation and weighted- residual error estimators, which provide reliable upper bounds for the energy error. Our analysis allows piecewise smooth parametrizations of the boundary, local mesh-refinement, and related standard piecewise polynomials as well as NURBS. We formulate an adaptive algorithm which steers the local mesh-refinement and the multiplicity of the knots. Numerical experiments show that the proposed adaptive strategy leads to optimal convergence, and related IGA boundary element methods are superior to standard boundary element methods with piecewise polynomials.

This technical memorandum presents two improved boundary element methods for predicting hydrodynamic coefficients of two dimensional sections. The first method is a source distribution method, while the second is a direct method for determining velocity potential. A major objective of these improved methods is to eliminate errors due to irregular frequencies, which currently exist in the close-fit method used by the strip theory program SHIPMO. Both new methods successfully eliminate problems caused by horizontal and vertical line segments with the close-fit method. To eliminate irregular frequencies of surface-piercing sections, the source distribution method employs additional sources on a deck lid at the waterline. The introduction of a deck lid eliminates some irregular frequencies but introduces new irregular frequencies. Alternatively, a modified direct method effectively eliminates all irregular frequencies. Future strip theory implementations should incorporate this modified direct method. This technical memorandum also reviews low and high frequency limits of hydrodynamic coefficients.

The Finite Element and Boundary Element Methods are described with their essential features illustrated using an example of a boundary value problem for a harmonic function. Analysis of the methodical errors is then carried out. This is followed by a consideration of the relative computational advantages of the two methods.

The Finite Element and Boundary Element Methods are described with their essential features illustrated using an example of a boundary value problem for a harmonic function. Analysis of the methodical errors is then carried out. This is followed by a consideration of the relative computational advantages of the two methods.

The Finite Element and Boundary Element Methods are described with their essential features illustrated using an example of a boundary value problem for a harmonic function. Analysis of the methodical errors is then carried out. This is followed by a consideration of the relative computational advantages of the two methods.

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This paper presents adaptive boundary element methods for positive, negative, as well as zero order operator equations, together with proofs that they converge at certain rates. The convergence rates are quasi-optimal in a certain sense under mild assumptions that are analogous to what is typically assumed in the theory of adaptive finite element methods. In particular, no saturation-type assumption is used. The main ingredients of the proof that constitute new findings are some results on a posteriori error estimates for boundary element methods, and an inverse-type inequality involving boundary integral operators on locally refined finite element spaces.

This report describes a method for computing solutions to partial differential equations in unbounded regions. The differential equations and unbounded regions arise in problems such as underwater acoustic and magnetic or electric fields surrounding vehicles or instruments in the sea or air. The method couples finite element and boundary integral equation solutions to compute shock response of submarine hulls, acoustic scattering due to elastic structures, electromagnetic signatures of ships and submarines, etc. The finite element method is used in the bounded region occupied by the vehicle or instrument. In this region there may be acoustic, magnetic or electric sources and the material properties may be nonuniform. The boundary integral equation method is used in the unbounded region occupied by the surrounding sea or atmosphere. This method requires that the unbounded region be assumed to be free of sources and have uniform material properties. The coupled method produced good results for a sample problem in which the temperature distribution was computed for a two-dimensional steady state heat flow. (Author)

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