Probabilistic domain decomposition (PDD) is an alternative paradigm for solving boundary
value problems (BVPs) in parallel with excellent scalability properties, thanks to its reliance …

State of the art domain decomposition algorithms for large-scale boundary value problems
(with M≫ 1 degrees of freedom) suffer from bounded strong scalability because they involve …

The numerical solution of large-scale PDEs, such as those occurring in data-driven
applications, unavoidably require powerful parallel computers and tailored parallel …

Abstract In a recent paper [7], a hybrid supercomputing algorithm for elliptic equations has
been proposed. The idea is that the interfacial nodal solutions solve a linear system, whose …

Despite its generality and powerful convergence properties, Milstein's method for functionals
of spatially bounded stochastic differential equations is widely regarded as difficult to …

The complex Helmholtz equation $(\Delta+ k^ 2) u= f $(where $ k\in {\mathbb R}, u (\cdot), f
(\cdot)\in {\mathbb C} $) is a mainstay of computational wave simulation. Despite its …

The dissertation focuses on addressing the challenges posed by multiscale problems in
applied mathematics, which stem from the intricate interplay between microscales and the …

This thesis is concerned with the construction and enhancement of algorithms involving
probability and statistics. The main motivation for these are problems that appear in finance …

In this paper, the probabilistic domain decomposition method is proposed for solving
numerically the Black-Scholes PDE. The main idea of the method consists of decoupling the …

The numerical solution of large-scale PDEs, such as those occurring in data-driven
applications, unavoidably require powerful parallel computers and tailored parallel …