Lect09-p2 - MeshGenerationandLoadBalancing...

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  Slide 1 / 19 Mesh Generation and Load Balancing CS 594 03/17/2010 Stan Tomov Innovative Computing Laboratory Computer Science Department The University of Tennessee March 17, 2010
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  Slide 2 / 19 Outline Motivation Background PDE simulation concept: approximation is over a mesh Error Analysis Simulation error: related to “local mesh size” Adaptive Mesh Generation Support parallel refinement/derefinement and “element migration” Load Balancing Scalability of the computation on modern architectures Data structures Algorithmically motivated: multigrid, domain decomposition, etc. For performance optimization: architecture aware computing Numerical Example  Conclusions
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  Slide 3 / 19 Motivation PDE simulations have  errors   stemming from the  numerical approximation (related to the mesh, . ..) The need for Reliable “error” to be less than desirable tolerance       and Efficient do not do “overkill” computation       PDE simulations for  High end computing systems .
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  Slide 4 / 19 Background In general: “Error” from the discretization is proportional to the mesh size A problem:  localized  physical phenomena deteriorate the approximation  properties of classical PDE approximations How can we find a “good” mesh, i.e. yielding  small and reliable error   and  efficient computation For example flows near wells; faults; moving fronts, etc.
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  Slide 5 / 19 Background Solution:   (1) determine (automatically) the regions of singular                          behaviour, and                    (2) refine them in a “balanced” manner Example: Efficiency of locally adapted vs uniform approximation of on an L-shaped domain r 1 / 2 sin θ / 2
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  Slide 6 / 19 Background Computational framework of the  Adaptive methods: i.e. a process of continuous feedback from the computation to find a reliable and efficient numerical PDE approximation Solve PDE Evaluate the approximation “error” Is “error”  acceptable Improve the approximation (h/p refinement) no yes done
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  Slide 7 / 19 Error Analysis The numerical solution of PDE (e.g. FEM) Boundary value problem:       Au      =  f ,    subject to boundary conditions Get a “weak” formulation:   (Au, 
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This note was uploaded on 04/01/2010 for the course COMPUTER S cs202 taught by Professor Jiuhui during the Spring '08 term at 東京国際大学.

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Lect09-p2 - MeshGenerationandLoadBalancing...

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