Catálogo de publicaciones - libros

Numerical simulations of coupled fluid-rigid solid problems by multigrid fictitious boundary and grid deformation methods are presented. The flow is computed by a special ALE formulation with a multigrid finite element solver. The solid body is allowed to move freely through the computational mesh which is adaptively aligned by a special mesh deformation method such that the accuracy for dealing with the interaction between the fluid and the solid body is highly improved. Numerical examples are provided to show the efficiency of the presented method.

We propose an iterative finite element method for solving non-linear hydromagnetic and steady Euler’s equations. Some three-dimensional computational tests are given to confirm the convergence and the high efficiency of the method.

The aim of this paper is to show the existence and present a numerical analysis of weak solutions for a quasi-linear elliptic problem with Dirichlet boundary conditions in a domain and data belonging to (). A numerical algorithm to compute a numerical approximation of the weak solution is described and analyzed. Numerical examples are presented and commented.

We use the -step technique proposed by Chronopoulos in [2, 3] for creating a -step variant of the Double Orthogonal Series algorithm (-DOS). The original Double Orthogonal Series algorithm, proposed by M. Amara and J. C. Nédélec [1], converges for any nonsingular coefficient matrix of the linear system in iterations at most, where is the order of the system. We prove the convergence of the new -DOS method in the integer part of / iterations at most.

The aim is to solve a linear equation in quaternions namely, the equation

The aim is to compute ASVD for large sparse matrices. In particular we will consider branches of selected singular values and the corresponding left/right singular vectors. We apply a predictor-corrector algorithm with an adaptive stepsize control.

In this paper, a new variant of the Jacobi-Davidson method is presented that is specifically designed for matrix pencils. Whenever a pencil has a complex conjugated pair of eigenvalues, the method computes the two dimensional real invariant subspace spanned by the two corresponding complex conjugated eigenvectors. This is beneficial for memory costs and in many cases it also accelerates the convergence of the JD method. In numerical experiments, the RJDQZ variant is compared with the original JDQZ method.

We evaluate the sparse grid solution technique [9, 4] with 4th order discretization for pricing multi-asset options. Convergence in the sense of point-wise interpolation to a special point is considered. We also present a novel variant based on backward differentiation formula coefficients. In combination with the high order discretization we can solve five-dimensional option pricing problems satisfactorily on coarse grids.

In this paper a new efficient linearly implicit time integrator for semilinear multidimensional parabolic problems is proposed. This method preserves the advantages, in terms of computational cost reduction, of the classical fractional step methods for linear parabolic problems.We show some numerical tests for illustrating that this method combined with standard space discretization techniques, provides efficient numerical algorithms capable of computing stable numerical solutions without restrictions between the time step and the mesh size.

Many physical processes can be modelled mathematically by ordinary differential equations. If such a process is governed by control variables an optimal control problem can be formulated. The basic problem is to choose the control variables such that some objective function is optimized while satisfying the differential equations. Approximating the control variables by linear functions and the state variables by low order Runge-Kutta schemes results in a nonlinear sparse constrained optimization problem. The inner iteration of a SQP-algorithm consists in solving an equality constrained quadratic optimization problem with a positive definite system matrix and a sparse constraint matrix. This optimization problem can be solved effectively by a projected cg-method when using a sparse LU decomposition of the constraint matrix.