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Regularized meshless method for boundary value problems with multiply-connected domain

Regularized meshless method for boundary value problems with multiply-connected domain. Jeng-Hung Kao Advisor: Jeng-Tzong Chen, Kue-Hung Chen 6, 29, 2006 HRE2-307. Outlines. Motivation and literature review Relation between MFS and RMM RMM for solving multiply-connected-domain problems

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Regularized meshless method for boundary value problems with multiply-connected domain

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  1. Regularized meshless method for boundary value problems with multiply-connected domain Jeng-Hung Kao Advisor: Jeng-Tzong Chen, Kue-Hung Chen 6, 29, 2006 HRE2-307 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  2. Outlines • Motivation and literature review • Relation between MFS and RMM • RMM for solving multiply-connected-domain problems • Application on multiply-connected-domain problems • Conclusions • Further research 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  3. Outlines • Motivation and literature review • Relation between MFS and RMM • RMM for solving multiply-connected-domain problems • Application on multiply-connected-domain problems • Conclusions • Further research 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  4. Motivation and literature review Numerical Methods • Motivation Mesh Methods Meshless Methods Finite Difference Method Finite Element Method Boundary Element Method (MFS) (RMM) 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  5. Motivation and literature review Meshless methods • literature review BEM FEM Singular kernel Continuous moving least square Continuous Kernel Nonsingular kernel MFS RMM Boundary collocation method Boundary node method Belyschko et al. 1994 Monagh 1982 Liu et al. 1995 Mukherjee, Huang, Chen & Kang 2002 EABE, IJNME Chen et al. 2002 JSV Kupradze 1964 CMMP Young and Chen 2005 JCP, JASA 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  6. Motivation and literature review • literature review d=0 Chen,Tanaka BKM onsingular general solution 2002 Helmholtz problem JT Chen BEM imaginary-part 2002 SW Kang NDIF imaginary-part 2002 Laplace problem Young and Chen RMM 2005 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  7. Motivation and literature review Exact solution 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  8. Motivation and literature review Convention MFS d=0.1 d=1.0 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  9. Motivation and literature review RMM 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  10. Outlines • Motivation and literature review • Relation between MFS and RMM • RMM for solving multiply-connected-domain problems • Application on multiply-connected-domain problems • Conclusions • Further research 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  11. Neumann problem Dirichlet problem Relation between MFS and RMM • Introduction of MFS Interior problem Exterior problem Kernel functions 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  12. Relation between MFS and RMM • Introduction of MFS Helmholtz problem Laplace problem Double-layer Potentials Single-layer Potentials 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  13. d=0 Relation between MFS and RMM • Introduction of MFS RMM Convention MFS 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  14. Relation between MFS and RMM • Introduction of RMM =0 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  15. Introduction of Method of Fundamental Solutions • Introduction of RMM 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  16. Relation between MFS and RMM • Compared RMM with MFS Single-layer potentialsDouble-layer potentials fictitiousboundary Real boundary Double-layer potentials Real boundary Real boundary 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  17. Outlines • Motivation and literature review • Relation between MFS and RMM • RMM for solving multiply-connected-domain problems • Application on multiply-connected-domain problems • Conclusions • Further research 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  18. Source point Collocation point RMM for solving multiply-connected-domain problems • Laplace problem 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  19. Source point Collocation point RMM for solving multiply-connected-domain problems • Laplace problem 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  20. Source point Collocation point RMM for solving multiply-connected-domain problems • Laplace problem 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  21. RMM for solving multiply-connected-domain problems • Construction of influence matrices 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  22. RMM for solving multiply-connected-domain problems • Test cases Neumann problem 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  23. RMM for solving multiply-connected-domain problems • Test cases 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  24. RMM for solving multiply-connected-domain problems • Test cases Arbitrary-shape problem 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  25. RMM for solving multiply-connected-domain problems • Test cases 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  26. Source point Collocation point RMM for solving multiply-connected-domain problems • Helmholtz problem 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  27. Source point Collocation point RMM for solving multiply-connected-domain problems • Helmholtz problem 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  28. Source point Collocation point RMM for solving multiply-connected-domain problems • Helmholtz problem 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  29. Source point Collocation point RMM for solving multiply-connected-domain problems • Helmholtz problem 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  30. RMM for solving multiply-connected-domain problems • Construction of influence matrices 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  31. SVD SVD RMM for solving multiply-connected-domain problems • SVD and SVD updating term Extracting out the eigenvalues Singular values matrix Treatments of spurious eigenvalues 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  32. RMM for solving multiply-connected-domain problems • Test case 8.87 (T) <8.88> 7.02 (T) <7.02> 4.44 (T) <4.44> 9.93 (T) <9.93> 11.33 (T) <11.33> 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  33. Outlines • Motivation and literature review • Relation between MFS and RMM • RMM for solving multiply-connected-domain problems • Application on multiply-connected-domain problems • Conclusions • Further research 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  34. Application on multiply-connected-domain problems • Antiplane shear problem • Antiplane piezoelectricity problem 0 0 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  35. Application on multiply-connected-domain problems • Decomposition of the problem 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  36. Application on multiply-connected-domain problems • Antiplane shear problems • Antiplane piezoelectricity problems Matrix Inclusion 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  37. Application on multiply-connected-domain problems • Compared antiplane piezoelectric with antiplane shear problems absent 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  38. Application on multiply-connected-domain problems • Compared antiplane piezoelectric with antiplane shear problems 0 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  39. Nm-2 Cm-2 CV-1m-1 Nm-2 Application on multiply-connected-domain problems • Antiplane piezoelectric problems with multiple inclusions 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  40. Application on multiply-connected-domain problems • Case 1: Single inclusion 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  41. Application on multiply-connected-domain problems • Case 1: Single inclusion 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  42. Nm-2 Cm-2 CV-1m-1 Nm-2 Application on multiply-connected-domain problems • Antiplane piezoelectric problems with multiple inclusions 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  43. d Application on multiply-connected-domain problems • Case 2: Two inclusions 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  44. Application on multiply-connected-domain problems • Case 2: Two inclusions d=10 d=0.1 d=1 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  45. Application on multiply-connected-domain problems • Case 2: Two inclusions d=10 d=1 d=0.1 d=0.02 d=0.01 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  46. Application on multiply-connected-domain problems • Antiplane shear problems with multiple inclusions Nm-2 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  47. Application on multiply-connected-domain problems • Case 1: Two inclusions 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  48. Application on multiply-connected-domain problems • Case 1: Two inclusions 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  49. Application on multiply-connected-domain problems • Antiplane shear problems with multiple inclusions 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

  50. Application on multiply-connected-domain problems • Case 2: Three inclusions 海洋大學力學聲響振動實驗室http://msvlab.hre.ntou.edu.tw

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