Domain decomposition methods coupled with parareal for the transient heat equation in 1 and 2 spatial dimensions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F20%3A10245877" target="_blank" >RIV/61989100:27240/20:10245877 - isvavai.cz</a>
Alternative codes found
RIV/61989100:27740/20:10245877
Result on the web
<a href="https://homel.vsb.cz/~luk76/publications/ApplMath19.pdf" target="_blank" >https://homel.vsb.cz/~luk76/publications/ApplMath19.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.21136/AM.2020.0219-19" target="_blank" >10.21136/AM.2020.0219-19</a>
Alternative languages
Result language
angličtina
Original language name
Domain decomposition methods coupled with parareal for the transient heat equation in 1 and 2 spatial dimensions
Original language description
We present a parallel solution algorithm for the transient heat equation in one and two spatial dimensions. The problem is discretized in space by the lowest-order conforming finite element method. Further, a one-step time integration scheme is used for the numerical solution of the arising system of ordinary differential equations. For the latter, the parareal method decomposing the time interval into subintervals is employed. It leads to parallel solution of smaller time-dependent problems. At each time slice a pseudostationary elliptic heat equation is solved by means of a domain decomposition method (DDM). In the 2d, case we employ a nonoverlapping Schur complement method, while in the 1d case an overlapping Schwarz DDM is employed. We document computational efficiency, as well as theoretical convergence rates of FEM semi-discretization schemes on numerical examples.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GA17-22615S" target="_blank" >GA17-22615S: Time reversal ultrasonic signal processing used in nondestructive evaluation of materials and structures</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Applications of Mathematics
ISSN
0862-7940
e-ISSN
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Volume of the periodical
65
Issue of the periodical within the volume
2
Country of publishing house
CZ - CZECH REPUBLIC
Number of pages
18
Pages from-to
173-190
UT code for WoS article
000525004700004
EID of the result in the Scopus database
2-s2.0-85083299526