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A diffusion-free multi-layer neural-network method for multidimensional nonlinear hyperbolic equations
Emmanuel Lorin, Arian Novruzi
This paper is devoted to the non-diffusive computation of solutions to -dimensional hyperbolic systems of conservation laws (HCL) and more specifically the accurate approximatio…
A Jin--Xin Relaxation Gradual Convergence Method for Conservation-Law PINNs
Emmanuel Lorin, Yuchong Tang, Xu Yang +1
The Jin--Xin relaxation of a nonlinear hyperbolic conservation law introduces a relaxation parameter that controls the width of the internal layer resolving a shock; the discontinu…
Non-diffusive neural network method for hyperbolic conservation laws
Emmanuel Lorin, Arian Novruzi
In this paper we develop a non-diffusive neural network (NDNN) algorithm for accurately solving weak solutions to hyperbolic conservation laws. The principle is to construct these…
A fast method for evaluating Volume potentials in the Galerkin boundary element method
Sasan Mohyaddin, Johannes Tausch
Three algorithm are proposed to evaluate volume potentials that arise in boundary element methods for elliptic PDEs. The approach is to apply a modified fast multipole method for a…