4 papers
A Filon-Clenshaw-Curtis-Smolyak rule for multi-dimensional oscillatory integrals with application to a UQ problem for the Helmholtz equation
Zhizhang Wu, Ivan G. Graham, Dingjiong Ma +1
In this paper, we combine the Smolyak technique for multi-dimensional interpolation with the Filon-Clenshaw-Curtis (FCC) rule for one-dimensional oscillatory integration, to obtain…
A multiscale reduced basis method for Schrödinger equation with multiscale and random potentials
Jingrun Chen, Dingjiong Ma, Zhiwen Zhang
The semiclassical Schrödinger equation with multiscale and random potentials often appears when studying electron dynamics in heterogeneous quantum systems. As time evolves, the wa…
A multiscale finite element method for the Schrödinger equation with multiscale potentials
Jingrun Chen, Dingjiong Ma, Zhiwen Zhang
In recent years, an increasing attention has been paid to quantum heterostructures with tailored functionalities, such as heterojunctions and quantum matematerials, in which quantu…
A model reduction method for multiscale elliptic PDEs with random coefficients using an optimization approach
Thomas Y. Hou, Dingjiong Ma, Zhiwen Zhang
In this paper, we propose a model reduction method for solving multiscale elliptic PDEs with random coefficients in the multiquery setting using an optimization approach. The optim…