The course presents numerical methods and algorithms for fundamental models in computational science, specifically particle models, ordinary differential equations and partial differential equations. Research topics are emphasised, e.g. regarding machine learning, parallel and distributed computing.
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Content and learning outcomes
The course focuses on three fields:
â€¢ 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.
â€¢ 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.
â€¢ 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.
Intended learning outcomes
After passing the course, the student should be able to:
â€¢ design and implement explicit time-step methods for particle models
â€¢ design and implement implicit time-step methods for general systems of ordinary differential equations (ODE)
â€¢ design and implement algorithms for systems of non-linear equations
â€¢ formulate finite element methods (FIVE) for partial differential equations (PDE) and adapt FEM software to a given problem
â€¢ Suggest appropriate parallelisation strategy for a given particle model ODE or PDE.
Literature and preparations
90 credits, of which 45 credits should be in mathematics and/or informatics.
Will be announced four weeks before the start of the course.
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
- LAB1 - Laboratory Assignments, 3.0 credits, grading scale: P, F
- TEN1 - Examination, 4.5 credits, grading scale: A, B, C, D, E, FX, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
Opportunity to complete the requirements via supplementary examination
Opportunity to raise an approved grade via renewed examination
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.
Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.Course web DD2363
Main field of study
In this course, the EECS code of honor applies, see: