1. Computational Mathematics in Mathematical 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 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

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)