Solution methods in computational mechanics - Course

Location: TUE

Coordinators: Jan ten Thije Boonkkamp, (TUE), Martijn Anthonissen (TUE)
Partial differential equations (PDEs) are ubiquitous in (fluid) mechanics, describing a
wide range of phenomena. This course will address some numerical methods for PDEs,
and consists of two parts, first, discretization and time integration methods, and second,
iterative methods for the resulting linear systems. The following topics are included:
• Classification of second order PDEs
• Finite difference methods for the Poisson equation (central differences, compact scheme)
• Finite volume methods for generic elliptic PDEs
• Advanced time integration methods for parabolic equations
• Discretisation methods for the wave equation (second and fourth order schemes)
• Basic iterative methods
• Krylov subspace methods
• Lanczos biorthogonalization
• Preconditioning
The discretization and time integration methods will be analysed in terms of accuracy
and stability. We like to emphasize that finite element methods are not covered in this
course. The course will include a number of computer sessions with MATLAB, in which
the participants can put in practice the numerical methods introduced. The required prior
knowledge is elementary numerical analysis.

For more information, contact:
Jan ten Thije Boonkkamp | 040 247 4123 | j.h.m.tenthijeboonkkamp@tue.nl

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