Differential Equations Solutions 181

Differential Equations Solutions 181 - Multiplication by P...

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Chapter 32 Solutions: Multigrid Methods: Managing Massive Meshes CHALLENGE 32.1. The V-cycle performs the following operations: η 1 Gauss–Seidel iterations for h =1 / 16: 15 η 1 multiplications (by h 2 / 2) h =1 / 16 residual evaluation 16 multiplications Multiplication by R 1 / 8 14 multiplications η 1 Gauss–Seidel iterations for h =1 / 8: 7 η 1 multiplications h =1 / 8 residual evaluation 8 multiplications Multiplication by R 1 / 4 6 multiplications η 1 Gauss–Seidel iterations for h =1 / 4: 3 η 1 multiplications h =1 / 4 residual evaluation 4 multiplications Multiplication by R 1 / 2 2 multiplications Direct solution of the system for h =1 / 2: 1 multiplication
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Unformatted text preview: Multiplication by P 1 / 2 2 multiplications 2 GaussSeidel iterations for h = 1 / 4: 3 2 multiplications Multiplication by P 1 / 4 6 multiplications 2 GaussSeidel iterations for h = 1 / 8: 7 2 multiplications Multiplication by P 1 / 8 14 multiplications 2 GaussSeidel iterations for h = 1 / 16: 15 2 multiplications The total cost is less than the cost of 2( 1 + 2 ) iterations, plus 2 residual calculations, all done on the h = 1 / 16 grid, plus 4 multiplications by R 1 / 8 . 191...
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This note was uploaded on 01/21/2012 for the course MAP 3302 taught by Professor Dr.robin during the Fall '11 term at University of Florida.

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