Probabilistic finite elements for nonlinear structural dynamics
Computer Methods in Applied Mechanics and Engineering
Generating optimal topologies in structural design using a homogenization method
Computer Methods in Applied Mechanics and Engineering
Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
A Fast Iterative Algorithm for Elliptic Interface Problems
SIAM Journal on Numerical Analysis
Effective Properties of Random Composites
SIAM Journal on Scientific Computing
A Finite Difference Method and Analysis for 2D Nonlinear Poisson-Boltzmann Equations
Journal of Scientific Computing
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
SIAM Journal on Numerical Analysis
Efficient stochastic Galerkin methods for random diffusion equations
Journal of Computational Physics
Journal of Computational and Applied Mathematics
| Hi-index | 7.29 |
In this work, we consider random elliptic interface problems, namely, the media in elliptic equations have both randomness and interfaces. A Galerkin method using bi-orthogonal polynomials is used to convert the random problem into an uncoupled system of deterministic interface problems. A principle on how to choose the orders of the approximated polynomial spaces is given based on the sensitivity analysis in random spaces, with which the total degree of freedom can be significantly reduced. Then immersed finite element methods are introduced to solve the resulting system. Convergence results are given both theoretically and numerically.