7 papers
Physics-informed token transformer methodology for nonlinear balance laws. I. Schwarzschild--Burgers fluid flows
Philippe G. LeFloch, Shuyang Xiang
We introduce a Physics-Informed Token Transformer (PITT) methodology for nonlinear hyperbolic balance laws in one space dimension, using piecewise steady-state profiles for the rep…
Physics-Informed Neural Networks for the Relativistic Burgers Equation in the Exterior of a Schwarzschild Black Hole
Shuyang Xiang
We introduce a Physics-Informed Neural Networks(PINN) to solve a relativistic Burgers equation in the exterior domain of a Schwarzschild black hole. Our main contribution is a PINN…
Embedded corrector problems for homogenization in linear elasticity
Virginie Ehrlacher, Frederic Legoll, Benjamin Stamm +1
In this article, we extend the study of embedded corrector problems, that we have previously introduced in the context of the homogenization of scalar diffusive equations, to the c…
Boundary integral equations for isotropic linear elasticity
Benjamin Stamm, Shuyang Xiang
This articles first investigates boundary integral operators for the three-dimensional isotropic linear elasticity of a biphasic model with piecewise constant Lamé coefficients in…
Existence theory for well-balanced Euler model
Shuyang Xiang, Yangyang Cao
We study the initial value problem for a kind of Euler equation with a source term. Our main result is the existence of a globally-in-time weak solution whose total variation is bo…
Weakly regular fluid flows with bounded variation on the domain of outer communication of a Schwarzschild black hole spacetime. A numerical study
Philippe G. LeFloch, Shuyang Xiang
We study the dynamical behavior of compressible fluids evolving on the outer domain of communication of a Schwarzschild background. To this end, we design several numerical methods…
Weakly regular fluid flows with bounded variation on a Schwarzschild background
Philippe G. LeFloch, Shuyang Xiang
We study the global dynamics of isothermal fluids evolving in the domain of outer communication of a Schwarzschild black hole. We first formulate the initial value problem within a…