caa a22 4500 475839803 CHVBK 20180406123858.0 cr unu---uuuuu 170329e20001101xx s 000 0 eng 10.1023/A:1004836400044 doi (NATIONALLICENCE)springer-10.1023/A:1004836400044 Application of polynomial preconditioners to conservation laws [Elektronische Daten] [Bernard Geurts, René van Buuren, Hao Lu] Polynomial preconditioners which are suitable in implicit time-stepping methods for conservation laws are reviewed and analyzed. The preconditioners considered are either based on a truncation of a Neumann series or on Chebyshev polynomials for the inverse of the system-matrix. The latter class of preconditioner is optimal in a space of polynomials of certain degree if the matrix has only real eigenvalues and a non-singular system of eigenvectors. The preconditioning can be applied to any convergent splitting of the system matrix, i.e. to any classical implicit time-stepping method for conservation laws that is based on a quasi-Newton iteration. An efficient implementation based on SSOR is presented and the approach is applied to simulations of the viscous unsteady Burgers equation and to inviscid steady flow around an airfoil in two spatial dimensions to illustrate the method in large-scale computations. For viscous flows the efficiency increase due to preconditioning is considerable. Kluwer Academic Publishers, 2000 polynomial preconditioning nationallicence conservation laws nationallicence implicit timestepping nationallicence aerodynamic flows nationallicence Geurts Bernard Faculty of Mathematical Scienes, University of Twente, P.O.Box217, 7500AE, Enschede, The Netherlands aut van Buuren René Faculty of Mathematical Scienes, University of Twente, P.O.Box217, 7500AE, Enschede, The Netherlands aut Lu Hao Institute for Scientific Computation, Texas A&M University, 77843-3404,, College Station, TX, U.S.A. aut Journal of Engineering Mathematics Kluwer Academic Publishers 38/4(2000-11-01), 403-426 0022-0833 38:4<403 2000 38 10665 https://doi.org/10.1023/A:1004836400044 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1004836400044 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Geurts Bernard Faculty of Mathematical Scienes, University of Twente, P.O.Box217, 7500AE, Enschede, The Netherlands aut NATIONALLICENCE 700 1- van Buuren René Faculty of Mathematical Scienes, University of Twente, P.O.Box217, 7500AE, Enschede, The Netherlands aut NATIONALLICENCE 700 1- Lu Hao Institute for Scientific Computation, Texas A&M University, 77843-3404,, College Station, TX, U.S.A aut NATIONALLICENCE 773 0- Journal of Engineering Mathematics Kluwer Academic Publishers 38/4(2000-11-01), 403-426 0022-0833 38:4<403 2000 38 10665 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer