Iterative solution of shifted positive-definite linear systems arising in a numerical method for the heat equation based on Laplace transformation and quadrature
McLean, William ; Thomee, Vidar
ANZIAM Journal, Tome 52 (2012), / Harvested from Australian Mathematical Society
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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. doi:10.1017/S1446181112000107

Publié le : 2012-01-01
DOI : https://doi.org/10.21914/anziamj.v53i0.5248 
@article{5248,
     title = {Iterative solution of shifted positive-definite linear systems arising in a numerical method for the heat equation based on Laplace transformation and quadrature},
     journal = {ANZIAM Journal},
     volume = {52},
     year = {2012},
     doi = {10.21914/anziamj.v53i0.5248},
     language = {EN},
     url = {http://dml.mathdoc.fr/item/5248}
}

McLean, William; Thomee, Vidar. Iterative solution of shifted positive-definite linear systems arising in a numerical method for the heat equation based on Laplace transformation and quadrature. ANZIAM Journal, Tome 52 (2012) . doi : 10.21914/anziamj.v53i0.5248. http://gdmltest.u-ga.fr/item/5248/