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Computational Mathematics in Mathematical Research --- My Experience

Computational Mathematics in Mathematical Research --- My Experience. Daniel Lee Tunghai University, Taiwan April 8 , 2014. Outlines. Beyond Mathematics Some Mathematics Essential Mathematics Applied Mathematics Conclusions. Beyond Mathematics Case 1. National D efense System C^3 I

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Computational Mathematics in Mathematical Research --- My Experience

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  1. Computational Mathematics inMathematical Research--- My Experience Daniel Lee Tunghai University, Taiwan April 8, 2014

  2. Outlines • Beyond Mathematics • Some Mathematics • Essential Mathematics • Applied Mathematics • Conclusions

  3. Beyond Mathematics Case 1 • National Defense System • C^3 I • command,control,communication,intelligence • War Game • My gains in Information Technology • conceptual design • system level know-how’s

  4. Some Mathematics Case 2 • CAD/CAM/CAE • Computer-Aided-Drafting • Computer-Aided-Design : AutoCad, CadKey • Computer-Aided-Manufacturing : SmartCam • Computer-Aided-Engineering : Pro-Engineer • My gains • program manager • know more spline applications : CAGD, SSI, … , etc. • know about … by Team Work • work right up to The Institution

  5. Essential MathematicsCase 3 • Computational Science, vs • Scientific Computing, vs • Scientific Computation . • Numerical Mathematics vs • Computational Mathematics • computational linear algebra • computational optimization/mathematical programing • computational ode/pde • computational signal and image processing • My gains : The Most Complicated Frontier • Multi-grid vs Multi-level • Parallel Computation via Domain Decomposition • data parallel vs functional parallel

  6. Conclusion • The wider the scope, the more freedom to success • The wider the scope, the longer lasting the system • The wider the scope, the more soft-tools • The wider the scope, the more useful math • The wider the scope, the little the pure math • The wider the scope, the easier the pure math • The wider the scope, good sol’s better than optimal sol’s • The wider the scope, the more challenging in many aspects

  7. Applied Mathematics -PU and THU • Free-Boundary Problem • Two-phase Solidification • with a mushy layer dynamics • computational Cauchy-convergence • Numerical Heart Modeling---ECG • Bio-Modeling of real life problem • Mathematical Model accordingly • Computational Model : continuous vs discrete • (Hex) FV-based FD approach • Proto-type via Matlab / Octave • Burning test : C-code(s)

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