Solution of singular elliptic PDEs on a union of rectangles using sinc methods.
Solving of heat shock on a hybrid system
Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs
The numerical approximation of parametric partial differential equations is a computational challenge, in particular when the number of involved parameter is large. This paper considers a model class of second order, linear, parametric, elliptic PDEs on a bounded domain D with diffusion coefficients depending on the parameters in an affine manner. For such models, it was shown in [9, 10] that under very weak assumptions on the diffusion coefficients, the entire family of solutions to such equations...
Spectral Approximation of the Periodic-Nonperiodic Navier-Stokes Equations.
Spectral element discretization of the heat equation with variable diffusion coefficient
We are interested in the discretization of the heat equation with a diffusion coefficient depending on the space and time variables. The discretization relies on a spectral element method with respect to the space variables and Euler's implicit scheme with respect to the time variable. A detailed numerical analysis leads to optimal a priori error estimates.
Spectral element discretization of the vorticity, velocity and pressure formulation of the Stokes problem
We consider the Stokes problem provided with non standard boundary conditions which involve the normal component of the velocity and the tangential components of the vorticity. We write a variational formulation of this problem with three independent unknowns: the vorticity, the velocity and the pressure. Next we propose a discretization by spectral element methods which relies on this formulation. A detailed numerical analysis leads to optimal error estimates for the three unknowns and numerical...
Spectral element discretization of the vorticity, velocity and pressure formulation of the Stokes problem
We consider the Stokes problem provided with non standard boundary conditions which involve the normal component of the velocity and the tangential components of the vorticity. We write a variational formulation of this problem with three independent unknowns: the vorticity, the velocity and the pressure. Next we propose a discretization by spectral element methods which relies on this formulation. A detailed numerical analysis leads to optimal error estimates for the three unknowns and numerical...
Spectral methods for singular perturbation problems
We study spectral discretizations for singular perturbation problems. A special technique of stabilization for the spectral method is proposed. Boundary layer problems are accurately solved by a domain decomposition method. An effective iterative method for the solution of spectral systems is proposed. Suitable components for a multigrid method are presented.
Spectral Methods with Sparse Matrices.
Spline collocation for strongly elliptic equations on the torus.
Spline qualocation methods for boundary integral equtions.
Strong convergence estimates for pseudospectral methods
Strong convergence estimates for pseudospectral methods applied to ordinary boundary value problems are derived. The results are also used for a convergence analysis of the Schwarz algorithm (a special domain decomposition technique). Different types of nodes (Chebyshev, Legendre nodes) are examined and compared.
Sweeping preconditioners for elastic wave propagation with spectral element methods
We present a parallel preconditioning method for the iterative solution of the time-harmonic elastic wave equation which makes use of higher-order spectral elements to reduce pollution error. In particular, the method leverages perfectly matched layer boundary conditions to efficiently approximate the Schur complement matrices of a block LDLT factorization. Both sequential and parallel versions of the algorithm are discussed and results for large-scale problems from exploration geophysics are presented....