Standard syllabus
Computational methods · Graduate · Math
Topics
Discretization frameworks
- Finite difference, finite volume, and finite element paradigms
- Consistency, stability, and convergence for discretizations
- CFL conditions and von Neumann analysis (introduction)
- Adaptive discretization strategies
- Meshless and particle methods (overview)
Linear and nonlinear solvers
- Sparse matrix storage and direct solvers
- Krylov methods and preconditioning in practice
- Newton–Krylov methods for nonlinear systems
- Multigrid and domain decomposition (introduction)
- Parallel algorithms and scalability basics
Time integration and optimization
- Explicit and implicit time-stepping for ODE/PDE systems
- Stiff problems and A-stable methods
- Optimal control discretization (introduction)
- PDE-constrained optimization (overview)
- Uncertainty quantification via sampling and surrogate models
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$1,162 · Computational methods · 18 tutoring hrs
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