Multilinear POD-DEIM model reduction for 2D and 3D semilinear systems of differential equations

<p style='text-indent:20px;'>We are interested in the numerical solution of coupled semilinear partial differential equations (PDEs) two and three dimensions. Under certain assumptions on domain, we take advantage Kronecker structure arising standard space discretizations operators illustrate how resulting system ordinary (ODEs) can be treated directly matrix or tensor form. Moreover, framework proper orthogonal decomposition (POD) discrete empirical interpolation method (DEIM) derive a two- three-sided model order reduction strategy that is applied to ODE form respectively. We discuss integrate reduced and, particular, solve tensor-valued linear at each timestep semi-implicit time discretization scheme. efficiency proposed through comparison existing techniques classical benchmark problems such as three-dimensional Burgers equation.</p>