DD2363 Methods in Scientific Computing
KTH Royal Institute of Technology
90 credits, of which 45 credits should be in mathematics and/or informatics.
The course focuses on three fields:
• Particle models. Explicit time-step methods, N-body problem and sparse approximations. Applications e g on the solar system, mass-spring systems or molecular dynamics.
• ODE models. Implicit time-step methods, algorithms for sparse systems of non-linear equations. Applications in e g population dynamics, system biology or chemical reactions.
• PDE models. Space discretisation through particles, structured grids or unstructured grids. Grid algorithms, refinement, coarsening, optimisation. Stencil methods, function approximation, Galerkin's method, the finite element method.
For each area, computer implementation and algorithms for parallel and distributed computation are discussed, which also is practiced in computer exercises.
After passing the course, the student should be able to:
• design and implement explicit time-step methods for particle models
• design and implement implicit time-step methods for general systems of ordinary differential equations (ODE)
• design and implement algorithms for systems of non-linear equations
• formulate finite element methods (FIVE) for partial differential equations (PDE) and adapt FEM software to a given problem
• Suggest appropriate parallelisation strategy for a given particle model ODE or PDE.
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