An Asymptotic Parallel-in-Time Method for Highly Oscillatory PDEs

An Asymptotic Parallel-in-Time Method for Highly Oscillatory PDEs

A combined Filon/asymptotic quadrature method for highly oscillatory problems

A cross between the asymptotic expansion of an oscillatory integral and the Filon-type methods is obtained by applying a Filon-type method on the error term in the asymptotic expansion, which is in itself an oscillatory integral. The efficiency of the approach is investigated through analysis and numerical experiments, and a potential for better methods than current ones is revealed. In particu...

Extended defect corrected averaging for highly oscillatory PDEs

We consider parabolic partial differential equations where the support of the sources or of the inhomogenous Neumann boundary conditions undergoes an oscillatory motion. The timescale of this oscillation is much smaller than the characteristic time scale of diffusion, which is of main interest. Resolution of the smallest timescale constitutes a strong restriction on the stepsize of time integra...

A Multiscale Finite Element Method for Pdes with Oscillatory Coefficients1

We present a multiscale finite element method (MFEM) for solving partial differential equations with highly oscillatory coefficients. MFEM provides a general and systematic framework for effectively capturing the large scale solutions without directly resolving the small scale details. This is accomplished by constructing the multiscale finite element base functions that are adaptive to the loc...

Parallel adaptive wavelet collocation method for PDEs

a r t i c l e i n f o a b s t r a c t Dynamic load balancing Wavelets Lifting scheme Second generation wavelets Adaptive grid Multiresolution Multilevel method Multigrid method Numerical method Partial differential equations Elliptic problem A parallel adaptive wavelet collocation method for solving a large class of Partial Differential Equations is presented. The parallelization is achieved by...