Iterative Solution of Shifted Positive-definite Linear Systems Arising in a Numerical Method for the Heat Equation Based on Laplace Transformation and Quadrature
نویسنده
چکیده
In earlier work we have studied a method for discretization in time of a parabolic problem, which consists of representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In application to a spatially semidiscrete finite-element version of the parabolic problem, at each quadrature point one then needs to solve a linear algebraic system having a positive-definite matrix with a complex shift. We study iterative methods for such systems, considering the basic and preconditioned versions of first the Richardson algorithm and then a conjugate gradient method. 2010 Mathematics subject classification: primary 65F10; secondary 65M22, 65M60, 65R10.
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