Splitting of Operators, Alternate Directions, and Paraxial Approximations for the Three-Dimensional Wave Equation
We design a family of new three-dimensional (3-D) paraxial equations well-adapted to numerical solution by the alternate directions method. These equations do not suffer from bad anisotropic effects and the cost for their numerical integration remains ...
Numerical Solution of a Nonlinear Dissipative System Using a Pseudospectral Method and Inertial Manifolds
We consider the numerical solution of nonlinear, dissipative partial differential equations using a pseudospectral method and the methodology of approximate inertial manifolds. Coarse and fine grids are employed, with a nonlinear mapping to relate the ...
A Pseudospectral Approach for Polar and Spherical Geometries
The singularities that arise in polar and spherical coordinates have in the past caused significant difficulties in obtaining accurate solutions to convection–diffusion-type problems in many fields (astrophysics, geophysics, meteorology, etc.). Viewing ...
Grid-Multipole Calculations
We describe new high-order, momentum conserving methods for spreading charge to and interpolating potential from the mesh. These methods permit efficient grid-based algorithms to be used in high-order accurate n-body particle codes such as the fast ...
On the Multigrid Waveform Relaxation Method
The multigrid waveform relaxation method is an efficient method for solving certain classes of time-dependent partial differential equations (PDEs). This paper studies the relationship between this method and the analogous multigrid method for steady-...
Parallel Domain-Oriented Multilevel Methods
Instead of the usual basis, we use a generating system for the discretization of elliptic partial differential equations (PDEs) that contains not only the basis functions of the finest level of discretization but additionally the basis functions of all ...
Least-Squares Mixed Finite Element Methods for Non-Selfadjoint Elliptic Problems: II. Performance of Block-ILU Factorization Methods
The least-squares mixed finite element technique developed in Part I is applied to non-selfadjoint second-order elliptic problems. This approach leads to a symmetric positive definite bilinear form which is coercive uniformly in the discretization ...
Optimal Convolution SOR Acceleration of Waveform Relaxation with Application to Parallel Simulation of Semiconductor Devices
In this paper we describe a novel generalized successive overrelaxation (SOR) algorithm for accelerating the convergence of the dynamic iteration method known as waveform relaxation. A new waveform convolution SOR algorithm is presented, along with a ...
A Direct Projection Method for Sparse Linear Systems
An oblique projection method is adapted to solve large, sparse, unstructured systems of linear equations. This row-projection technique is a direct method which can be interpreted as an oblique Kaczmarz-type algorithm, and is also related to other ...
Numerical Shadowing Near Hyperbolic Trajectories
Shadowing is a means of characterizing global errors in the numerical solution of initial value ordinary differential equations by allowing for a small perturbation in the initial condition. The method presented in this paper allows for a perturbation in ...
A Limited Memory Algorithm for Bound Constrained Optimization
An algorithm for solving large nonlinear optimization problems with simple bounds is described. It is based on the gradient projection method and uses a limited memory BFGS matrix to approximate the Hessian of the objective function. It is shown how to ...
Best Constrained Approximation in Hilbert Space and Interpolation by Cubic Splines Subject to Obstacles
We review a Lagrangian parameter approach to problems of best constrained approximation in Hilbert space. The variable is confined to a closed convex subset of the Hilbert space and is also assumed to satisfy linear equalities. The technique is applied to ...
Efficient Detection of a Continuous-Wave Signal with a Linear Frequency Drift
An efficient method is presented for the detection of a continuous-wave (CW) signal with a frequency drift that is linear in time. Signals of this type occur if the transmitter and receiver are rapidly accelerating with respect to one another, for example,...
