Constitutive Equatios Technische Universiteit Eindhoven 本构方程埃因霍温理工大学.pptVIP

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Constitutive Equatios Technische Universiteit Eindhoven 本构方程埃因霍温理工大学.ppt

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Constitutive Equatios Technische Universiteit Eindhoven 本构方程埃因霍温理工大学

Local Defect Correctionfor the Boundary Element Method Outline Introduction BEM LDC Why LDC for BEM Coarse grid problem Fine grid problem The local defect Defect correction and the Algorithm Numerical experiments and results Conclusions and future work Introduction: BEM Why LDC for BEM Coarse grid problem Fine grid problem The local defect Defect correction and the Algorithm Numerical experiments and results Results Conclusions THANK YOU. * * Kakuba Godwin CASA day, Tuesday May 9, 2006 The solution of a function is expressed in terms of its values and values of its normal derivatives at the boundary in an integral equation. Problem ?2u = 0 in ?, given u or ?nu at ??. Discretisation: Elements in the boundary (mother equation) Coarse grid solution Fine grid solution ? Large error Defect BCs dH 0 in ? BCs on ?? LDC Problems with high local activity Uniform grids Full matrices i j Discretisation Uniform triangular elements Constant elements Solution: H H/2 H/2 Ah l AH c = Solution: uh l,0 , , For we have two solutions, coarse and fine grid solutions AHuH = bH ??H l ? = c AH AH l + defect Defect correction The Algorithm Initialisation Solve the basic coarse grid problem Solve the local fine grid problem Iterations i = 1,2,… Solve the updated coarse grid problem Solve the local fine grid problem for i = 1,2,… Test problem 4 6 10 Let be the size of the global problem, the size of the local problem, the number of ??lH nodes Composite problem complexity: Complexity of the BEMLDC algorithm: ? Factor 2 reduction in complexity Same accuracy as the uniform grid whose size is equivalent to the grid size of the local problem Reduced complexity by a factor 2 Future work Practical problem Convergence Next Global coarse grid error Back Updated global coarse grid error Back Updated global coarse grid error Back * * *