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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 Î· 2 Gaussâ€“Seidel iterations for h = 1 / 4: 3 Î· 2 multiplications Multiplication by P 1 / 4 6 multiplications Î· 2 Gaussâ€“Seidel iterations for h = 1 / 8: 7 Î· 2 multiplications Multiplication by P 1 / 8 14 multiplications Î· 2 Gaussâ€“Seidel iterations for h = 1 / 16: 15 Î· 2 multiplications The total cost is less than the cost of 2( Î· 1 + Î· 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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