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 Defense System C^3 I command,control,communication,intelligence War Game My gains in Information Technology conceptual design system level know-how’s

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

Essential Mathematics Case 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

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

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)