Structure preserving integration and model order reduction of skew gradient reaction diffusion systems
Yazarlar (3)
Bülent Karasözen
Middle East Technical University (Metu), Türkiye
Middle East Technical University (Metu), Türkiye
Tuğba Kkseyhan
Middle East Technical University (Metu), Türkiye
Middle East Technical University (Metu), Türkiye
Prof. Dr. Murat UZUNCA Middle East Technical University (Metu), Türkiye
| Makale Türü | Özgün Makale (SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale) | ||
| Dergi Adı | Annals of Operations Research (Q2) | ||
| Dergi ISSN | 0254-5330 Dergi Bilgileri (2017) | ||
| Dergi Tarandığı Indeksler | SCI | ||
| Makale Dili | İngilizce | Basım Tarihi | 10-2017 |
| Cilt / Sayı / Sayfa | 258 / 1 / 79–106 | DOI | 10.1007/s10479-015-2063-6 |
| Makale Linki | http://link.springer.com/10.1007/s10479-015-2063-6 | ||
| UAK Araştırma Alanları |
Uygulamalı Matematik
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| Özet |
| Activator-inhibitor FitzHugh–Nagumo (FHN) equation is an example for reaction–diffusion equations with skew-gradient structure. We discretize the FHN equation using symmetric interior penalty discontinuous Galerkin (SIPG) method in space and average vector field (AVF) method in time. The AVF method is a geometric integrator, i.e. it preserves the energy of the Hamiltonian systems and energy dissipation of the gradient systems. In this work, we show that the fully discrete energy of the FHN equation satisfies the mini-maximizer property of the continuous energy for the skew-gradient systems. We present numerical results with traveling fronts and pulses for one dimensional, two coupled FHN equations and three coupled FHN equations with one activator and two inhibitors in skew-gradient form. Turing patterns are computed for fully discretized two dimensional FHN equation in the form of spots and labyrinths … |
| Anahtar Kelimeler |
| Discontinuous Galerkin | Discrete empirical interpolation | Energy preservation | FitzHugh–Nagumo equations | Gradient systems | Model order reduction | Traveling fronts and pulses | Turing patterns |
BM Sürdürülebilir Kalkınma Amaçları
| Atıf Sayıları | |
| Web of Science | 6 |
| Scopus | 6 |
| Google Scholar | 17 |