4 citations · 7 across the 5 of their papers we have counts for
9 papers
An iterative method for Helmholtz boundary value problems arising in wave propagation
Francisco Bernal, Xingyuan Chen, Goncalo dos Reis
The complex Helmholtz equation (where ) is a mainstay of computational wave simulation. Despite its apparent simplici…
A Radial Basis Function Partition of Unity Method for Steady Flow Simulations
Francisco Bernal, Ali Safdari-Vaighani, Elisabeth Larsson
A methodology is presented for the numerical solution of nonlinear elliptic systems in unbounded domains, consisting of three elements. First, the problem is posed on a finite doma…
A hybrid probabilistic domain decomposition algorithm suited for very large-scale elliptic PDEs
Francisco Bernal, Jorge Morón-Vidal, Juan A. Acebrón
State of the art domain decomposition algorithms for large-scale boundary value problems (with degrees of freedom) suffer from bounded strong scalability because they invo…
A policy iteration algorithm for nonzero-sum stochastic impulse games
René Aïd, Francisco Bernal, Mohamed Mnif +2
This work presents a novel policy iteration algorithm to tackle nonzero-sum stochastic impulse games arising naturally in many applications. Despite the obvious impact of solving s…
An implementation of Milstein's method for general bounded diffusions
Francisco Bernal
Despite its generality and powerful convergence properties, Milstein's method for functionals of spatially bounded stochastic differential equations is widely regarded as difficult…
Multilevel estimation of expected exit times and other functionals of stopped diffusions
Michael B. Giles, Francisco Bernal
This paper proposes and analyses a new multilevel Monte Carlo method for the estimation of mean exit times for multi-dimensional Brownian diffusions, and associated functionals whi…
Hybrid PDE solver for data-driven problems and modern branching
Francisco Bernal, Gonçalo dos Reis, Greig Smith
The numerical solution of large-scale PDEs, such as those occurring in data-driven applications, unavoidably require powerful parallel computers and tailored parallel algorithms to…
Solving delay differential equations through RBF collocation
Francisco Bernal, Gail Gutiérrez
A general and easy-to-code numerical method based on radial basis functions (RBFs) collocation is proposed for the solution of delay differential equations (DDEs). It relies on the…
Trust-Region Methods for Nonlinear Elliptic Equations with Radial Basis Functions
Francisco Bernal
We consider the numerical solution of nonlinear elliptic boundary value problems with Kansa's method. We derive analytic formulas for the Jacobian and Hessian of the resulting nonl…