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This is Part 2 of a report-pair concerning application of the tensor product in solving large sets of simultaneous linear equations arising in finite element formulations of Numerical Weather Prediction problems. A rectangular region having a graded mesh with Dirichlet boundary conditions on all four edges is considered. Coefficient matrices are the mass matrix and the stiffness matrix of the finite element method. For the stiffness matrix, which appears in Poisson's equation, operation counts and storage requirements are compared with corresponding numbers for solutions by successive overrelaxation and Gaussian elimination. FORTRAN programs for implementation of the tensor proeuct formulations are given. (Author)

This report concerns application of the tensor product in solving large sets of linear equations arising in Numerical Weather Prediction problems. The coefficient matrix considered is called the 'mass' matrix in finite element parlance. Theory of the tensor product resolution is presented, along with methods for imposing Dirichlet and cyclic boundary conditions. Operation counts and storage requirements are compared with corresponding numbers for some widely-used solution algorithms. Listings of Fortran programs for implementing the tensor product solution system (TENSOR) and testing it are given.

Report for period April 1984 - June 1984.--pt.2

Final report for period October 1982 - September 1983.--pt.1

Final report for period October 1982 - September 1983.--pt.1

Report for period April 1984 - June 1984.--pt.2

1Opticks

By Sir Isaac Newton

The famous physicist Sir Isaac Newton lectured on optics from 1670 - 1672. He worked on refraction of light into colored beams using prisms and discovered chromatic aberration. He also postulated the corpuscular form of light and an ether to transmit forces between the corpuscles. His "Opticks", first published 1704 contains his postulates about the topic. This is the fourth edition in English, from 1730, which Newton himself had corrected from the third edition before his death. (Summary by Availle)

The life of Doctor Johnson, told in his own words and (mostly) those of others around him. "Anyone with a teaspoonful of imagination can read this play with pleasure; with two teaspoonsful, I will not be responsible for results. He, or she, may be disappointed, for there is no plot to speak of. But there is talk - about as good talk as has ever been reported, and James Boswell as a reporter has never had an equal. (The Author)" - Summary by ToddHW <BR><BR>Cast list:<BR> ACT 1: <a href=""></a><br> Mr. STEWART: <a href="https://librivox.org/reader/13489">James Thomas</a><br> Mr. MAITLAND: <a href="https://librivox.org/reader/10789">Tomas Peter</a><br> Mr. MACBEAN: <a href="https://librivox.org/reader/7170">alanmapstone</a><br> Mr. LEVETT: <a href="https://librivox.org/reader/13285">Mike Casey</a><br> Dr. JOHNSON: <a href="https://librivox.org/reader/10801">Jim Locke</a><br> A VOICE (MACPHERSON'S): <a href="https://librivox.org/reader/13661">Lynette Caulkins</a><br> Mr. BOSWELL: <a href="https://librivox.org/reader/13072">Campbell Schelp</a><br> A SERVANT (LORD CHESTERFIELD'S): <a href="https://librivox.org/reader/12874">Aaron White</a><br> Mrs. WILLIAMS: <a href="https://librivox.org/reader/13257">Elsie Selwyn</a><br> FRANK (DR. JOHNSON'S COLORED SERVANT): <a href="https://librivox.org/reader/11535">Nemo</a><br> Mr. ALLEN: <a href="https://librivox.org/reader/13577">Adrian Stephens</a><br> Mrs. WOFFINGTON: <a href="https://librivox.org/reader/10087">Sandra Schmit</a><br> BET FLINT: <a href="https://librivox.org/reader/10614">Leanne Yau</a><br> POLL CARMICHAEL: <a href="https://librivox.org/reader/11417">Eva Davis</a><br> Mrs. THRALE: <a href="https://librivox.org/reader/12500">Foon</a><br> : <a href=""></a><br> ACT 2: <a href=""></a><br> Mrs. THRALE: <a href="https://librivox.org/reader/12500">Foon</a><br> JUDSON: <a href="https://librivox.org/reader/10614">Leanne Yau</a><br> Footman: <a href="https://librivox.org/reader/13403">Philip Watson</a><br> RATTLE: <a href="https://librivox.org/reader/11417">Eva Davis</a><br> Miss BURNEY: <a href="https://librivox.org/reader/10179">Sonia</a><br> Mr. MURPHY: <a href="https://librivox.org/reader/12874">Aaron White</a><br> Sir JOSHUA REYNOLDS: <a href="https://librivox.org/reader/7170">alanmapstone</a><br> Mr. GARRICK: <a href="https://librivox.org/reader/10789">Tomas Peter</a><br> Dr. JOHNSON: <a href="https://librivox.org/reader/10801">Jim Locke</a><br> Mr. THRALE: <a href="https://librivox.org/reader/13563">Steven Fellows</a><br> Dr. GOLDSMITH: <a href="https://librivox.org/reader/13577">Adrian Stephens</a><br> General PAOLI: <a href="https://librivox.org/reader/13661">Lynette Caulkins</a><br> Mr. BOSWELL: <a href="https://librivox.org/reader/13072">Campbell Schelp</a><br> Miss MORE: <a href="https://librivox.org/reader/13257">Elsie Selwyn</a><br> Miss STREATFIELD: <a href="https://librivox.org/reader/10087">Sandra Schmit</a><br> Mrs. DELANEY: <a href="https://librivox.org/reader/4174">Availle</a><br> Mr. BARETTI: <a href="https://librivox.org/reader/12428">Pier</a><br> : <a href=""></a><br> ACT 3: <a href=""></a><br> Dr. JOHNSON: <a href="https://librivox.org/reader/10801">Jim Locke</a><br> A SERVANT (Dr. Johnson's): <a href="https://librivox.org/reader/12874">Aaron White</a><br> RATTLE: <a href="https://librivox.org/reader/11417">Eva Davis</a><br> Mrs. THRALE: <a href="https://librivox.org/reader/12500">Foon</a><br> Mr. BOSWELL: <a href="https://librivox.org/reader/13072">Campbell Schelp</a><br> Mr. BARCLAY: <a href="https://librivox.org/reader/10789">Tomas Peter</a><br> Mr. PERKINS: <a href="https://librivox.org/reader/13577">Adrian Stephens</a><br> Miss BURNEY: <a href="https://librivox.org/reader/10179">Sonia</a><br> Miss THRALE: <a href="https://librivox.org/reader/10614">Leanne Yau</a><br> : <a href=""></a><br> ACT 4: <a href=""></a><br> Dr. JOHNSON: <a href="https://librivox.org/reader/10801">Jim Locke</a><br> FRANK (DR. JOHNSON'S COLORED SERVANT): <a href="https://librivox.org/reader/11535">Nemo</a><br> Mrs. DESMOULINS: <a href="https://librivox.org/reader/10087">Sandra Schmit</a><br> Mr. HOOLE: <a href="https://librivox.org/reader/12874">Aaron White</a><br> MARY WOLLSTONECRAFT: <a href="https://librivox.org/reader/13257">Elsie Selwyn</a><br> Sir JOSHUA REYNOLDS: <a href="https://librivox.org/reader/7170">alanmapstone</a><br> Mrs. SIDDONS: <a href="https://librivox.org/reader/11417">Eva Davis</a><br> Dr. BROCKLESBY: <a href="https://librivox.org/reader/10789">Tomas Peter</a><br> Mr. WINDHAM: <a href="https://librivox.org/reader/13577">Adrian Stephens</a><br> Miss BURNEY: <a href="https://librivox.org/reader/10179">Sonia</a><br> Mr. BURKE: <a href="https://librivox.org/reader/13563">Steven Fellows</a><br> YOUNG GIRL: <a href="https://librivox.org/reader/10614">Leanne Yau</a><br> Stage Directions and Editing: <a href="https://librivox.org/reader/6754">ToddHW</a>

3Observations Upon the Apocalypse of St. John

By Sir Isaac Newton

While Isaac Newton is most known today for his research in physics, during his own life he was also well-known for his religious scholarship. Engaging in intensive research on Christian history, theology, and the Bible, Newton cared deeply about understanding his faith. Among Newton's writings are those on prophecies described in the Bible. Here, he analyzes the last book of the New Testament - Revelation AKA the Apocalypse of St. John - in order to gain an understanding of the world's end times. He seems especially interested in tracking how post-Jesus Roman history compares with the events described in Revelation. Observations Upon the Apocalypse of St. John was posthumously published in 1733, as part of Newton's larger work on Bible prophecy. (Summary by Adam Bielka)

John Newton, best known for his hymn "Amazing Grace", for his former life as a slave trader and as eventual opponent of the slave trade in Britain. These 14 short letters cover his early life to about 1755 and are filled with his Christian reflections on the events of his life. Letter 5 contains Newton's description of his life under Amos Clowe, an enslaver, who gave him to his wife as a servant. It is worth noting that this collection was published in 1764 and Newton did not publish his scathing pamphlet Thoughts Upon the Slave Trade until 1788 and thus his letters focus on his life as a "an infidel and libertine" (Newton's own description) than on the institution he later condemned. - Summary by InTheDesert

The celebrated German-British composer G.F. Handel premiered his now famous oratorio "Messiah" in 1742. In 1785 there was a celebration at Westminster Abbey of Handel's birth 100 years before. It was on this occasion that John Newton decided to preach 50 sermons from the Bible passages that form the libretto (by Charles Jennens) of Messiah. The sermons were preached over two years in the Parish Church of St. Mary Woolnoth, Lombard-Street - 3 miles from Westminster Abbey. - Summary by InTheDesert

Four Letters to a Minister of an Independent Church by a Minister of the Church of England<br> Quid me alta silentia cogis rumpere? - Virgil ("Why force me to break the deep silence?")<br><br> Let us therefore follow after the things which make for peace, and things wherewith one may edify another. For in Jesus Christ, neither circumcision availeth any thing, nor uncircumcision; but faith which worketh by love — Rom. xiv.19 Gal. v.6<br> First printed in 1764 - Summary by Title Page

7Double Crossed

By Wilfrid Douglas Newton

Clement Seadon is a young man of free spirit and a lust for a life of independence. However after receiving an odd request from a lawyer he is compelled to involve himself in the prevention of a dangerous plot to swindle an heiress. - Summary by Howard Skyman

Among the excellences which appear in all the published letters of Newton, we may mention:<br>In the first place, the grand design — the high and holy object which he seems to propose in all he speaks and writes, and which never seems absent from his mind. Another trait in Mr. N’s. character as a letterwriter, and which imparts great interest as well as utility to his writings, is, his knowledge of human nature, and his close observation of men and things. There is in Newton’s letters, a style and manner of composition admirably suited to the nature and objects of epistolary communications. But that which forms the most prominent feature in the charter of these letters is the uncommon degree of experimental knowledge of the power of godliness, which they every where exhibit. - Summary by E.P. Swift

A Review of Ecclesiastical History, so far as it Concerns the Progress, Declension, and Revivals of Evangelical Doctrine and Practice ; with a Brief Account of the Spirit and Methods by which Vital and Experimental Religion Have Been Opposed in all Ages of the Church - Summary by Title Page