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航空航天 > 麻省理工学院：《偏微分方程式数字方法》（英文版）Lecture 7 Iterative Method
麻省理工学院：《偏微分方程式数字方法》（英文版）Lecture 7 Iterative Method
Background Developed over the last 25 years- Brandt (1973) published first paper with practical results Offers the possibility of solving a problem with work and storage proportional to the number of unknowns Well developed for linear elliptic problems application to other equations is still an active area of research
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Restriction Basic Principles Given wn we obtain w2h by restriction 2h= Th 2h200 C2h: restriction operator(matrix) Simplest procedure is injection 021,2=,2fori=1,,n21 SMA-HPC⊙2003MT Iterative Methods: Multigrid Techniques 10
Restriction Basic Principles Intuitively 2h GOOD BAD SMA-HPC⊙2003MT Iterative Methods: Multigrid Techniques 11
Restriction Basic Principles If we write Uk: eigenvectors of A h Ck U Only the modes k =1, are "visible" by grid 2h 2 visible"by grid 2h aliased m-1m+1 2 SMA-HPC⊙2003MT Iterative Methods: Multigrid Techniques 12
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