Multiscale methods for evolution problems
Doktorsavhandling, 2023
At first, the localized orthogonal decomposition framework is extended to the strongly damped wave equation, where two different highly varying coefficients are present (Paper~I). The dependency of the solution on the different coefficients vary with time, which the proposed method accounts for automatically. Then we consider a parabolic equation where the diffusion is rapidly varying in both time and space (Paper~II). Here, the framework is extended so that the modified finite element space uses space-time basis functions that contain the information of the diffusion coefficient. Furthermore, we study wave propagation problems posed on spatial networks (Paper~III). Such systems are characterized by a matrix with large variations inherited from the underlying network. For this purpose, an LOD based approach adapted to general matrix systems is considered. Finally, we analyze the framework for a parabolic stochastic PDE with multiscale characteristics (Paper~IV). In all papers we prove error estimates for the methods, and confirm the theoretical findings with numerical examples.
localized orthogonal decomposition
multiscale
stochastic partial differential equations
Strongly damped wave equation
finite element method
spatial network models
parabolic equations
Författare
Per Ljung
Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik
Ämneskategorier
Beräkningsmatematik
ISBN
978-91-7905-842-5
Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 5308
Utgivare
Chalmers
Pascal
Opponent: Olof Runborg, KTH, Sweden