Numerical Linear Algebra with Applications · 2004 · 46 citations · 22 references
ComputingComputational EngineeringElectrical EngineeringFinite Element AnalysisFinite Element MethodsSemiconductor DevicesDevice ModelingDevice SimulationFinite Element DiscretizationIterative SolversMixed Finite Element MethodsParallel Numerical MethodsFinite Element Device SimulationFinite Element SimulationIterative Methods For Linear SystemsNumerical Device SimulationNumerical SimulationParallel SolversSemiconductor Device ModelingSemiconductor Technology
The numerical simulation of semiconductor devices is extremely demanding in term of computational time because it involves complex embedded numerical schemes. At the kernel of these schemes is the solution of very ill-conditioned large linear systems. In this paper, we present the various ingredients of some hybrid iterative schemes that play a central role in the robustness of these solvers when they are embedded in other numerical procedures. On a set of two-dimensional unstructured mixed finite element problems representative of semiconductor simulation, we perform a fair and detailed comparison between parallel iterative and direct linear solution techniques. We show that iterative solvers can be robust enough to solve the very challenging linear systems that arise in those simulations. Copyright © 2004 John Wiley & Sons, Ltd.
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The Algebraic Eigenvalue Problem
E. I., J. H. Wilkinson · Mathematics of Computation · 1966 · 5.2K citations