Randolph E. Bank

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This software is made available for research and instructional use only. You may copy and use this software without charge for these non-commercial purposes, provided that the copyright notice and associated text is reproduced on all copies. For all other uses (including distribution of modified versions), please contact the author. This software is(More)
We make a theoretical study of the application of a standard hierarchical basis multigrid iteration to the convection diiusion equation, discretized using an upwind nite element discretizations. We show behavior that in some respects is similar to the symmetric positive deenite case, but in other respects is markedly diierent. In particular, we nd the rate(More)
In this paper, we present an overview of the physical principles and numerical methods used to solve the coupled system of nonlinear partial differential equations that model the transient behavior of silicon VLSI device structures. We also describe how the same techniques are applicable to circuit simulation. A composite linear multistep formula is(More)
In this paper, the multilevel ILU (MLILU) decomposition is introduced. During an incomplete Gaussian elimination process new matrix entries are generated such that a special ordering strategy yields distinct levels. On these levels, some smoothing steps are computed. The MLILU decomposition exists and the corresponding iterative scheme converges for all(More)
The choice of basis functions for a nite element space has important consequences in the practical implementation of the nite element method. A traditional choice is the nodal or Lagrange basis. Many of the computational advantages of this basis derive from the property of compact support enjoyed by the basis functions. Here we study a second choice, the(More)
We present a new approach to the use of parallel computers with adaptive finite element methods. This approach addresses the load balancing problem in a new way, requiring far less communication than current approaches. It also allows existing sequential adaptive PDE codes such as PLTMG and MC to run in a parallel environment without a large investment in(More)
In this paper, we prove the convergence of the multilevel iterative methods for solving linear equations that arise from elliptic partial diierential equations. Our theory is presented entirely in terms of the generalized condition number of the matrix A and the smoothing matrix B. This leads to a completely algebraic analysis of the method as in iterative(More)
The Bi-Conjugate Gradient (BCG) algorithm is the simplest and most natural generalization of the classical conjugate gradient method for solving nonsymmetric linear systems. It is well-known that the method suffers from two kinds of breakdowns. The first is due to the breakdown of the underlying Lanczos process and the second is due to the fact that some(More)