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Direct solvers are a common method for solving finite difference frequencydomain (FDFD) systems that arise in numerical solutions of Maxwell's equations.In a direct solver, one factorizes the system matrix. Since the system matrixis typically very sparse, the fill-in of these factors is the single mostimportant computational consideration in terms of time complexity and memoryrequirements. As a result, it is of great interest to determine ways in whichthis fill-in can be systematically reduced. In this paper, we show that in thecontext of commonly used perfectly matched boundary layer methods, the choiceof boundary condition behind the perfectly matched boundary layer can beexploited to reduce fill-in incurred during the factorization, leading tosignificant gains of up to 40 percent in the efficiency of the factorizationprocedure. We illustrate our findings by solving linear systems and eigenvalueproblems associated with the FDFD method.

optics express

Effect of Choices of Boundary Conditions on the Numerical Efficiency of  Direct Solutions of Finite Difference frequency Domain Systems with Perfectly  Matched Layers