Sokołowski, Jan - ed. ; Sonnendrücker, Eric - ed.
Computers are becoming sufficiently powerful to permit to numerically solve problems such as the wave equation with high-order methods. In this article we will consider Lagrange finite elements of order k and show how it is possible to automatically generate the mass and stiffness matrices of any order with the help of symbolic computation software. We compare two high-order time discretizations: an explicit one using a Taylor expansion in time (a Cauchy-Kowalewski procedure) and an implicit Runge-Kutta scheme. ; We also construct in a systematic way a high-order quadrature which is optimal in terms of the number of points, which enables the use of mass lumping, up to P5 elements. We compare computational time and effort for several codes which are of high order in time and space and study their respective properties.
Zielona Góra: Uniwersytet Zielonogórski
AMCS, volume 17, number 3 (2007) ; kliknij tutaj, żeby przejść
Biblioteka Uniwersytetu Zielonogórskiego
2024-04-03
2024-04-03
23
https://zbc.uz.zgora.pl/publication/88416
Nazwa wydania | Data |
---|---|
Arbitrary high-order finite element schemes and high-order mass lumping | 2024-04-03 |
Albers, Bettina Savidis, Atavros A. Taşan, Ercan H. Estorff, Otto von Gehlken, Malte Cordón, Oskar - ed. Kazienko, Przemysław - ed.
Sharma, Avadesh Kumar Chauhan, Premanand Singh Sharma, P. Bhadoria, Shailendra Singh Jurczak, Paweł - red.
Czechowski, Leszek Jurczak, Paweł - red.
Strug, Barbara Paszyńska, Anna Paszyński, Maciej Grabska, Ewa Korbicz, Józef - red. Uciński, Dariusz - red.
Szafran, Jacek Juszczyk-Andraszyk, Klaudia Kamiński, Marcin Jurczak, Paweł - red.
Kuczma, Mieczysław Wybranowska, Krystyna Świtka, Romuald - red.
Różyło, Patryk Wysmulski, Paweł Falkowicz, Katarzyna Jurczak, Paweł - red.
Daşdemir, Ahmet Jurczak, Paweł - red.