SIAM Journal on Scientific Computing

In a three-dimensional isotropic elastic earth, the wave equation solution consists of three velocity components and six stresses. We discretize the partial derivatives using second order in time and fourth order in space staggered finite difference ...

A modification is given of the GMRES iterative method for nonsymmetric systems of linear equations. The new method deflates eigenvalues using Wu and Simon's thick restarting approach [SIAM J. Matrix Anal. Appl., 22 (2000), pp. 602--616]. It has the ...

The classical Schwarz method is a domain decomposition method to solve elliptic partial differential equations in parallel. Convergence is achieved through overlap of the subdomains. We study in this paper a variant of the Schwarz method which converges ...

In this paper we introduce an effective algebraic method for the computation of all the stationary points of the squared distance $d^2$ between a point on one ellipse and a point on a second ellipse with a focus in common with the first one.

This problem ...

Singular and hypersingular operators are ubiquitous in problems of physics, and their use requires a careful numerical interpretation. Although analytical methods for their regularization have long been known, the classical approach does not provide ...

A new adaptive mesh movement strategy is presented, which, unlike many existing moving mesh methods, targets the mesh velocities rather than the mesh coordinates. The mesh velocities are determined in a least squares framework by using the geometric ...

While the Chebyshev pseudospectral method provides a spectrally accurate method, integration of partial differential equations with spatial derivatives of order M requires time steps of approximately $O(N^{-2M})$ for stable explicit solvers. Theoretically,...

Nonreflecting boundary conditions for problems of wave propagation are nonlocal in space and time. While the nonlocality in space can be efficiently handled by Fourier or spherical expansions in special geometries, the arising temporal convolutions still ...

Inexact Newton algorithms are commonly used for solving large sparse nonlinear system of equations $F(u^{\ast})=0$ arising, for example, from the discretization of partial differential equations. Even with global strategies such as linesearch or trust ...

In a semiorthogonal Lanczos algorithm, the orthogonality of the Lanczos vectors is allowed to deteriorate to roughly the square root of the rounding unit, after which the current vectors are reorthogonalized. A theorem of Simon [Linear Algebra Appl., 61 (...

A front tracking method for inviscid gas dynamics is presented. The key constructions and algorithms used in the code are described and the interrelations between shock capturing, interface dynamics, computational geometry, grid construction, and ...

We present a new method for solving the sparse linear system of equations arising from the discretization of the linearized steady-state Navier--Stokes equations (also known as the Oseen equations). The solver is an iterative method of Krylov subspace ...

The fast Gauss transform of L. Greengard and J. Strain [SIAM J. Sci. Statist. Comput., 12 (1991), pp. 79--94] reduces the computational complexity of the evaluation of the sum of N Gaussians at M points in d-dimensional space from ${\cal O}(MN)$ to ${\cal ...

A recursive method of constructing preconditioning matrices for the nonsymmetric stiffness matrix in a wavelet basis is proposed for solving a class of integral and differential equations. It is based on a level-by-level application of the wavelet scales ...

One approach to solving the nonsymmetric eigenvalue problem in parallel is to parallelize the QR algorithm. Not long ago, this was widely considered to be a hopeless task. Recent efforts have led to significant advances, although the methods proposed up ...

In this paper, we present an inverse free Krylov subspace method for finding some extreme eigenvalues of the symmetric definite generalized eigenvalue problem $Ax = \lambda B x$. The basic method takes a form of inner-outer iterations and involves no ...

We report a class of stabilized explicit-implicit domain decomposition (SEIDD) methods for the numerical solution of parabolic equations. Explicit-implicit domain decomposition (EIDD) methods are globally noniterative, nonoverlapping domain decomposition ...