Convergence and stability analysis of heterogeneous time step coupling schemes for parabolic problems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F17%3A00312563" target="_blank" >RIV/68407700:21110/17:00312563 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.sciencedirect.com/science/article/pii/S0168927417301617" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0168927417301617</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.apnum.2017.07.003" target="_blank" >10.1016/j.apnum.2017.07.003</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Convergence and stability analysis of heterogeneous time step coupling schemes for parabolic problems

Popis výsledku v původním jazyce

We propose and rigorously analyze the subcycling method based on primal domain decomposition techniques for first-order transient partial differential equations. In time dependent problems, it can be computationally advantageous to use different time steps in different regions. Smaller time steps are used in regions of significant changes in the solution and larger time steps are prescribed in regions with nearly stationary response. Subcycling can efficiently reduce the total computational cost. Crucial to our approach is a nonstandard heterogeneous temporal discretization. We begin with the discretization in time by the asynchronous Rothe method, which, in essence, involves a backward finite difference scheme assuming different time steps (fine and large time steps) in different parts of the computational domain. The emphasis of the paper is on qualitative properties of the new numerical scheme, such as a-priori estimates, existence of the time-discrete solutions and the strong convergence and stability analysis. Several numerical experiments were conducted to examine the consistency of the proposed method.

Název v anglickém jazyce

Convergence and stability analysis of heterogeneous time step coupling schemes for parabolic problems

Popis výsledku anglicky

We propose and rigorously analyze the subcycling method based on primal domain decomposition techniques for first-order transient partial differential equations. In time dependent problems, it can be computationally advantageous to use different time steps in different regions. Smaller time steps are used in regions of significant changes in the solution and larger time steps are prescribed in regions with nearly stationary response. Subcycling can efficiently reduce the total computational cost. Crucial to our approach is a nonstandard heterogeneous temporal discretization. We begin with the discretization in time by the asynchronous Rothe method, which, in essence, involves a backward finite difference scheme assuming different time steps (fine and large time steps) in different parts of the computational domain. The emphasis of the paper is on qualitative properties of the new numerical scheme, such as a-priori estimates, existence of the time-discrete solutions and the strong convergence and stability analysis. Several numerical experiments were conducted to examine the consistency of the proposed method.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA14-21450S" target="_blank" >GA14-21450S: Efektivní asynchronní numerické metody pro sdružené procesy ve stavebních konstrukcích a geomateriálech</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Applied Numerical Mathematics

ISSN

0168-9274

e-ISSN

1873-5460

Svazek periodika

121

Číslo periodika v rámci svazku

November

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

25

Strana od-do

198-222

Kód UT WoS článku

000410013800013

EID výsledku v databázi Scopus

2-s2.0-85026543430