l40 - Lecture 40: Introduction to Multigrid Methods 1 Last...

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1 Lecture 40: Introduction to Multigrid Methods
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2 Last Time… Completed co-located SIMPLE problem
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3 This Time… We will: Consider performance of Jacobi and Gauss-Seidel schemes for different types of initial guesses Exploit this fact in devising multigrid schemes
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4 Gauss-Seidel and Jacobi Schemes Gauss-Seidel and Jacobi schemes represented by the iteration: Latest available value for Gauss-Seidel Previous iteration value for Jacobi
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5 Unstructured Gauss-Seidel Pseudo Code
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6 General Iterative Methods General principle of all iterative methods is » Given current iterate x k , we wish to find a better approximation x k+1 Error in any iteration k is: Of course we don’t know x, so we don’t know the error But we can find out how well the current iterate satisfies our linear system by looking at the residual:
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7 Error Equation Premultiplying by A yields the error equation: Since The error equation can also be written as: kk  e x x
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8 General Iterative Scheme
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l40 - Lecture 40: Introduction to Multigrid Methods 1 Last...

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