High-Order Methods Applied to Nonlinear Magnetostatic Problems

Reduced order modeling techniques for numerical homogenization methods applied to linear and nonlinear multiscale problems

The characteristic of effective properties of physical processes in heterogeneous media is a basic modeling and computational problem for many applications. As standard numerical discretization of such multiscale problems (e.g. with classical finite element method (FEM)) is often computationally prohibitive, there is a need for a novel computational algorithm able to capture the effective behav...

Exponentially fitted methods applied to fourth-order boundary value problems

Fourth-order boundary value problems are solved by means of exponentially-fitted methods of different orders. These methods, which depend on a parameter, can be constructed following a six-step flow chart of Ixaru and Vanden Berghe. Special attention is paid to the expression of the error term and to the choice of the parameter in order to make the error as small as possible. Some numerical exa...

High-order Boltzmann machines applied to the Monk's problems

Derivative-free high-order methods applied to preliminary orbit determination

From position and velocity coordinates for several given instants, it is possible to determine orbital elements for the preliminary orbit. This theoretical trajectory, also known as keplerian orbit, is defined taking only into account mutual gravitational attraction forces between both bodies, the Earth and the satellite. Nevertheless it should be refined with later observations from ground sta...

Parallel computation of three-dimensional nonlinear magnetostatic problems

We describe a general-purpose parallel electromagnetic code for computing accurate solutions to large computationally demanding, 3D, nonlinear magnetostatic problems. The code, CORAL, is based on a volume integral equation formulation. Using an IBM SP parallel computer and iterative solution methods, we successfully solved the dense linear systems inherent in such formulations. A key component ...