A reversible multiscale integration method

Heterogeneous Multiscale Finite Element Method with Novel Numerical Integration Schemes

In this paper we introduce two novel numerical integration schemes, within the framework of the heterogeneous multiscale method (HMM) when finite element method is used as the macroscopic solver, to resolve the elliptic problem with multiscale coefficient. For non-self-adjoint elliptic problems, optimal convergence rate is proved for the proposed methods, which naturally yields a new strategy f...

Heterogeneous Multiscale Finite Element Method with Novel Numerical Integration Schemes

In this paper we introduce two novel numerical integration schemes, within the framework of the heterogeneous multiscale method (HMM) when finite element method is used as the macroscopic solver, to resolve the elliptic problem with multiscale coefficient. For non-self-adjoint elliptic problems, optimal convergence rate is proved for the proposed methods, which naturally yields a new strategy f...

Equation Free Projective Integration: A multiscale method applied to a plasma ion acoustic wave

Multiscale problems such as magnetic reconnection and turbulence are notoriously hard to simulate because the physics of micro and macroscales are strongly linked. This study is the first application of a novel numerical scheme called Equation Free Projective Integration (EFPI) to a plasma system: we simulate the propagation and steepening of a 1D ion acoustic wave. In EFPI, the simulations act...

A Multiscale Discontinuous Galerkin Method

We propose a new class of Discontinuous Galerkin (DG) methods based on variational multiscale ideas. Our approach begins with an additive decomposition of the discontinuous finite element space into continuous (coarse) and discontinuous (fine) components. Variational multiscale analysis is used to define an interscale transfer operator that associates coarse and fine scale functions. Compositio...

A Numerical Integration Method by Using Generalized Series of Functions