In this paper we propose and analyze a stochastic collocation method to solve elliptic partial
differential equations with random coefficients and forcing terms (input data of the model) …

This paper aims to provide a comprehensive review of the state-of-the-art modeling and
optimization methods for multi-scale heterogeneous lattice structures (MSHLS) to further …

This work proposes and analyzes a stochastic collocation method for solving elliptic partial
differential equations with random coefficients and forcing terms. These input data are …

Theory and Applications has been very successful and was well received by the
computational science community worldwide, so a 2nd edition has become necessary eight …

This paper develops a robust framework for the multiscale design of three-dimensional
lattices with macroscopically tailored structural characteristics. The work exploits the high …

Mathematical models of radiation carcinogenesis are important for understanding
mechanisms and for interpreting or extrapolating risk. There are two classes of such …

We study Poisson equations and averaging for Stochastic Differential Equations (SDEs).
Poisson equations are essential tools in both probability theory and partial differential …

This paper studies the compression of partial differential operators using neural networks.
We consider a family of operators, parameterized by a potentially high-dimensional space of …

The insatiable demand to optimize and engineer new functionalities in electromagnetic
devices has risen their geometrical complexity to unprecedented levels. This usually results …

In this paper, we present a new Monte-Carlo methodology referred to as Adaptive Fup
Monte-Carlo Method (AFMCM) based on compactly supported Fup basis functions and a …