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math.NA2023
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…
math.NA2023
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…
math.NA2023
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…