Zobrazeno 1 - 10
of 17
pro vyhledávání: '"Zachary J. Grant"'
Publikováno v:
Communications on Applied Mathematics and Computation. 5:97-115
We develop and use a novel mixed-precision weighted essentially non-oscillatory (WENO) method for solving the Teukolsky equation, which arises when modeling perturbations of Kerr black holes. We show that WENO methods outperform higher-order finite-d
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9b04399cb57eca87fded06615ee0db7d
https://doi.org/10.1007/s42967-021-00129-2
https://doi.org/10.1007/s42967-021-00129-2
Publikováno v:
SIAM Journal on Numerical Analysis. 58:3197-3225
High order methods are often desired for the evolution of ordinary differential equations, in particular those arising from the semidiscretization of partial differential equations. In prior work w...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d63e68cbfb7370407c5a8b95d694d018
https://doi.org/10.1137/19m1306129
https://doi.org/10.1137/19m1306129
Additive Runge-Kutta methods designed for preserving highly accurate solutions in mixed-precision computation were proposed and analyzed in [8]. These specially designed methods use reduced precision or the implicit computations and full precision fo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6089e57e43be53aed7d7101d5079b763
http://arxiv.org/abs/2107.03357
http://arxiv.org/abs/2107.03357
Publikováno v:
Journal of Scientific Computing. 81:1446-1471
Problems with components that feature significantly different time scales, where the stiff time-step restriction comes from a linear component, implicit-explicit (IMEX) methods alleviate this restriction if the concern is linear stability. However, w
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::37cf0363aeada4d31b0933ddb43981bd
https://doi.org/10.1007/s10915-019-01046-6
https://doi.org/10.1007/s10915-019-01046-6
In this work we present a class of high order unconditionally strong stability preserving (SSP) implicit multi-derivative Runge--Kutta schemes, and SSP implicit-explicit (IMEX) multi-derivative Runge--Kutta schemes where the time-step restriction is
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7122a64d0fe8380a86c11d3a91e3dcb1
In simulations of fluid motion time accuracy has proven to be elusive. We seek highly accurate methods with strong enough stability properties to deal with the richness of scales of many flows. These methods must also be easy to implement within curr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dce9576a7c8ed16b4ca3a76cac48b3af
Publikováno v:
SIAM Journal on Numerical Analysis. 56:3276-3307
Strong stability preserving (SSP) Runge-Kutta methods are often desired when evolving in time problems that have two components that have very different time scales. Where the SSP property is needed, it has been shown that implicit and implicit-expli
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ffab3ebec38c1327ffe2e4aa4cf64c54
https://doi.org/10.1137/17m1143290
https://doi.org/10.1137/17m1143290
Publikováno v:
Pure and Applied Mathematics Quarterly. 14:3-25
Strong stability preserving (SSP) Runge-Kutta methods are desirable when evolving in time problems that have discontinuities or sharp gradients and require nonlinear non-inner-product stability properties to be satisfied. Unlike the case for L2 linea
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::82ab36a8862d1e9f7ca1a006136cf360
https://doi.org/10.4310/pamq.2018.v14.n1.a1
https://doi.org/10.4310/pamq.2018.v14.n1.a1
Autor:
Sigal Gottlieb, Zachary J. Grant, Christopher Bresten, Daniel Higgs, Adrián Németh, David I. Ketcheson
Publikováno v:
Mathematics of Computation. 86:747-769
High-order spatial discretizations with strong stability properties (such as monotonicity) are desirable for the solution of hyperbolic PDEs. Methods may be compared in terms of the strong stability preserving (SSP) time-step. We prove an upper bound
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::098ba0a8614c44b1945c92ec8eaae2de
https://doi.org/10.1090/mcom/3115
https://doi.org/10.1090/mcom/3115
Publikováno v:
Journal of Open Source Software. 5:2514
Much of the initial RK-Opt development was performed by D. Ketcheson while he was supported by a DOE Computational Science Graduate Fellowship and by AFOSR grant number FA9550-06-1-0255. Development has also been supported by funding from King Abdull
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::4e4b4cbfb263b5d41084ad4deeaca627
https://doi.org/10.21105/joss.02514
https://doi.org/10.21105/joss.02514