MultigridIntro

MultigridIntro - Complexity of direct methods n 1/2 n 1/3...

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Administrivia: November 18, 2009 Administrivia: November 18, 2009 Course project progress reports due next Monday. Reading in Multigrid Tutorial: Chapters 3-4: Multigrid cycles and implementation Chapter 5: Multigrid convergence (next time) Chapter 8: Algebraic multigrid (for next Wednesday)
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Complexity of linear solvers Complexity of linear solvers 2D 3D Sparse Cholesky: O(n 1.5 ) O(n 2 ) CG, exact arithmetic: O(n 2 ) O(n 2 ) CG, no precond: O(n 1.5 ) O(n 1.33 ) CG, modified IC: O(n 1.25 ) O(n 1.17 ) CG, support trees: O(n 1.20 ) O(n 1.31 ) CG, Spielman/Teng: O(n 1+ε ) O(n 1+ε ) Multigrid: O(n) O(n) n 1/2 n 1/3 Time to solve model problem (Poisson’s equation) on regular mesh
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Complexity of direct methods
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Unformatted text preview: Complexity of direct methods n 1/2 n 1/3 2D 3D Space (fill): O(n log n) O(n 4/3 ) Time (flops): O(n 3/2 ) O(n 2 ) Time and space to solve any problem on any well-shaped finite element mesh Multigrid Multigrid (introduction) (introduction) • Find an approximate solution on a coarser mesh, and then improve it on a finer mesh • Reduce smooth fine-mesh error by using coarse mesh again • Use idea recursively on hierarchy of meshes • Solves the model problem (Poisson’s eqn) in linear time! • Often useful when hierarchy of meshes can be built • This is just the intuition – lots of theory and technology...
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This note was uploaded on 12/27/2011 for the course CMPSC 290h taught by Professor Chong during the Fall '09 term at UCSB.

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MultigridIntro - Complexity of direct methods n 1/2 n 1/3...

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