A High-Order, Conservative Integrator with Local Time-Stepping
- Creators
- Throwe, William
- Teukolsky, Saul
Abstract
We present a family of multistep integrators based on the Adams--Bashforth methods. These schemes can be constructed for arbitrary convergence order with arbitrary step size variation. The step size can differ between different subdomains of the system. It can also change with time within a given subdomain. The methods are linearly conservative, preserving a wide class of analytically constant quantities to numerical roundoff, even when numerical truncation error is significantly higher. These methods are intended for use in solving conservative PDEs in discontinuous Galerkin formulations or in finite-difference methods with compact stencils. A numerical test demonstrates these properties and shows that significant speed improvements over the standard Adams--Bashforth schemes can be obtained.
Additional Information
© 2020 Society for Industrial and Applied Mathematics. Submitted to the journal's Methods and Algorithms for Scientific Computing section October 11, 2019; accepted for publication (in revised form) September 21, 2020; published electronically December 1, 2020. This work was partially supported by the Sherman Fairchild Foundation and by NSF through grants PHY-1606654 and ACI-1713678.Attached Files
Published - 19m1292692.pdf
Submitted - 1811.02499.pdf
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Additional details
- Eprint ID
- 98091
- Resolver ID
- CaltechAUTHORS:20190821-155551404
- Sherman Fairchild Foundation
- PHY-1606654
- NSF
- ACI-1713678
- NSF
- Created
-
2019-08-21Created from EPrint's datestamp field
- Updated
-
2021-11-16Created from EPrint's last_modified field
- Caltech groups
- Astronomy Department