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"A thoughtful consideration of the current level of development of multigrid methods, this volume is a carefully edited collection of papers that addresses its topic on several levels. The first three chapters orient the reader who is familiar with standard numerical techniques to multigrid methods, first by discussing multigrid in the context of standard techniques, second by detailing the mechanics of use of the method, and third by applying the basic method to some current problems in fluid dynamics. The fourth chapter provides a unified development, complete with theory, of algebraic multigrid (AMG), which is a linear equation solver based on multigrid principles. The last chapter is an ambitious development of a very general theory of multigrid methods for variationally posed problems. Included as an appendix is the latest edition of the Multigrid Bibliography, an attempted compilation of all existing research publications on multigrid."

"Diskritisasi persoalan yang berbentuk persamaan diferensial dapat menghasilkan sistem persamaan linier (terlinierisasi) Au = d, dimana matrik koefisien A berupa matrik tridiagonal. Tulisan ini membicarakan alternatif solusi sistem persamaan tersebut, metode reduksi ganjil-genap siklis (cyclic odd-even reduction) dan pemisahan rekursif (recursive decoupling), pada sistem multiprosesor. Ide dasar metode reduksi siklis adalah menurunkan baris-baris independen dengan cara reduksi pada baris berindek ganjil atau genap. Metode pemisahan rekursif berdasarkan strategi perubahan rank-satu (rank-one updating), dan partisi sistem matrik menjadi submatrik 2x2. Aplikasi metode tersebut diimplementasikan pada sistem multiprosesor berbasis transputer. Kinerja algoritma paralel dievaluasi berdasarkan parameter waktu eksekusi (running time), granularitas, percepatan (speed-up), efisiensi, dan biaya. Secara kualitatif algoritma reduksi siklis memiliki granularitas yang kecil (cenderung fine grain) dibandingkan granularitas algoritma pemisahan rekursif yang relatif besar (coarse grain). Dari eksperimen hingga 8 prosesor diperoleh peningkatan kecepatan sebesar 1,77 {2 prosesor) sampai 4,22 (8 prosesor) untuk algoritma reduksi siklis, dan algoritma pemisahan rekursif sebesar 2,00 (2 prosesor) hingga 5,90 (8 prosesor). Sedangkan efisiensinya, algoritma reduksi siklis mencapai 88,38 persen (2 prosesor) dan 52,78 persen (8 prosesor). Untuk algoritma pemisahan rekursif efisiensinya mencapai 100 persen (2 prosesor) dan 73,82 persen (8 prosesor). Hasil optimal dicapai algoritma pemisahan rekursif pada implementasi memakai 2 prosesor, dengan percepatan sama dengan 2, efisiensi 100 persen, dan biaya yang diperlukan sama dengan biaya eksekusi memakai satu prosesor."

"Multilevel adaptive methods play an increasingly important role in the solution of many scientific and engineering problems. Fast adaptive methods techniques are widely used by specialists to execute and analyze simulation and optimization problems. This monograph presents a unified approach to adaptive methods, addressing their mathematical theory, efficient algorithms, and flexible data structures."

"A practical handbook for understanding and using fast adaptive composite grid (FAC) methods for discretization and solution of partial differential equations (PDEs). Contains fundamental concepts. These so-called FAC are characterized by their use of a composite grid, which is nominally the union of various uniform grids. FAC is capable of producing a composite grid with tailored resolution, and a corresponding solution with commensurate accuracy, at a cost proportional to the number of composite grid points. Moreover, special asynchronous versions of the fast adaptive composite grid methods (AFAC) studied here have seemingly optimal complexity in a parallel computing environment. Most of the methods treated in this book were discovered only within the last decade, and in many cases their development is still in its infancy. While this is not meant to be comprehensive, it does provide a theoretical and practical guide to multilevel adaptive methods and relevant discretization techniques. It also contains new material, which is included to fill in certain gaps and to expose new avenues of research. Also, because adaptive refinement seems to demand a lot of attention to philosophical issues, personal perspectives are often brought freely into the discussion."

"This second edition of the popular A Multigrid Tutorial preserves the introductory spirit of the first edition while roughly doubling the amount of material covered. The topics of the first edition have been enhanced with additional discussion, new numerical experiments, and improved figures. New topics in the second edition include nonlinear equations, Neumann boundary conditions, variable mesh and variable coefficient problems, anisotropic problems, algebraic multigrid (AMG), adaptive methods, and finite elements."

"The multilevel projection method is a new formalism that provides a framework for the development of multilevel algorithms in a very general setting. This methodology guides the choices of all the major multilevel processes, including relaxation and coarsening, and it applies directly to global or locally-refined discretizations."