|»|| Scientific Computing Group
|»|| Special topics
||Model order reduction, numerical linear algebra||
Scientific Computing Group
Scientific Computing is a fast-growing, highly interdisciplinary field
that brings together methods from numerical analysis, high-performance
computing and various application fields. It is the area of research
that provides better simulation tools aimed at many different
Many of our current application areas are energy-related:
Other application areas to which our research is directed are:
- Wind-turbine and wind-farm aerodynamics,
- Tokamak magnetohydrodynamics,
- Plasma-assisted combustion,
- Battery technologies,
- Porous media flows,
- Electronic circuits,
Numerical methods on which we currently do research:
- Fluid-structure interactions,
- Hypervelocity impacts,
- Shape optimization.
- Symplectic time-integration methods,
- Physics-compatible finite-volume methods (exponential schemes, multi-D upwind schemes, limiters, ...),
- Generalized Krylov methods,
- Evolutionary design algorithms.
Some of the active research in more detail
Complete flux based finite volume schemes
Many applications give rise to mathematical models with partial differential equations of advection-diffusion-reaction type. These equations describe conservation of mass, momentum, energy and alike.
Applications we work on include combustion and plasma physics.
A possibility for the computation of numerical fluxes in these applications is to use an exponential scheme. These schemes have the same accuracy for all Reynolds numbers in flow problems.
Furthermore, exponential schemes preserve monotonicity properties of the exact solution.
Smoothed particle hydrodynamics (SPH)
Particle Hydrodynamics (SPH) is a numerical method that is successfully
applied in science and engineering.
Since it is a gridless, particle-based technique, it is especially
suited for treating problems with free surfaces, multiphase flow,
high-velocity impact, crack propagation and large deformations.
SPH is a Lagrangian method in which the
state of the system is represented by a set of particles. These
interact with their neighbors; the range of interaction is controlled
by a smooth kernel function. Field variables such as
density, velocity and acceleration are calculated from the particle
SPH is easy to implement.
The resulting equations can be solved in a straightforward manner and allow
The numerical approximation of
many scientific and engineering problems leads to
block-structured indefinite linear systems in saddle point form. These
systems originate from for instance conservation laws, constrained
optimization problems, mixed
finite element discretizations and generalized least squares
problems. The successful design of robust, scalable and efficient
preconditioners is intimately connected with an understanding of the
structure of the resulting block matrix system and relies heavily on
exploiting this structure.
Model order reduction (MOR)
MOR is a method to capture dominant features of problems, enabling much faster simulation. It
aids realistic simulations of multi-aspect problems.
Special algorithms have been developed for
dominant pole algorithms,
nonlinear oscillators and more.
Inverse and ill-posed problems
Many problems in science and engineering lead o inverse problems that may be ill-posed: there are many solutions, or the solution may be very sensitive with respect to change in the input data. We develop efficient generic methods for these problems, for instance based on new and improved variants of Tikhonov regularization.
Generalized Krylov methods
Krylov methods are very suitable techniques for solving important large-scale linear algebra problems such as linear systems, eigenvalue problems, and model reduction. We develop new variants of Krylov methods that are tailored to solve challenging problems.
Large nonlinear problems are often solved by Newton methods. In these Newton methods a large system has to be solved in every step, which is computationally expensive. We propose methods to solve these linear systems inexactly, so that the solution is obtained faster.