A general convergence result for a functional related to the theory of homogenization
SIAM Journal on Mathematical Analysis
Homogenization and two-scale convergence
SIAM Journal on Mathematical Analysis
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
A multiscale finite element method for elliptic problems in composite materials and porous media
Journal of Computational Physics
Wavelet-Based Numerical Homogenization
SIAM Journal on Numerical Analysis
Computing
Fourth Order Chebyshev Methods with Recurrence Relation
SIAM Journal on Scientific Computing
A general strategy for designing seamless multiscale methods
Journal of Computational Physics
A multiscale cell boundary element method for elliptic problems
Applied Numerical Mathematics
A multiscale hp-FEM for 2D photonic crystal bands
Journal of Computational Physics
Optimal spatiotemporal reduced order modeling, Part I: proposed framework
Computational Mechanics
| Hi-index | 31.46 |
In this paper, we propose a numerical method, the finite difference heterogeneous multi-scale method (FD-HMM), for solving multi-scale parabolic problems. Based on the framework introduced in [Commun. Math. Sci. 1 (1) 87], the numerical method relies on the use of two different schemes for the original equation, at different grid level which allows to give numerical results at a much lower cost than solving the original equations. We describe the strategy for constructing such a method, discuss generalization for cases with time dependency, random correlated coefficients, nonconservative form and implementation issues. Finally, the new method is illustrated with several test examples.