We present an approach for solving optimal boundary control problems of nonlinear optics
by using deep learning. For computing high resolution approximations of the solution to the …

We present a space–time Trefftz discontinuous Galerkin method for approximating the
acoustic wave equation semi-explicitly on tent pitched meshes. DG Trefftz methods use …

We introduce a space–time Trefftz discontinuous Galerkin method for the first-order transient
acoustic wave equations in arbitrary space dimensions, extending the one-dimensional …

We present a space–time ultra-weak discontinuous Galerkin discretization of the linear
Schrödinger equation with variable potential. The proposed method is well-posed and quasi …

A space-time Trefftz discontinuous Galerkin method for the Schrödinger equation with
piecewise-constant potential is proposed and analyzed. Following the spirit of Trefftz …

Abstract In Trefftz discontinuous Galerkin methods a partial differential equation is
discretized using discontinuous shape functions that are chosen to be elementwise in the …

Trefftz methods are high-order Galerkin schemes in which all discrete functions are
elementwise solution of the PDE to be approximated. They are viable only when the PDE is …

We develop a convergence theory of space–time discretizations for the linear, second-order
wave equation in polygonal domains, possibly occupied by piecewise homogeneous media …

We study the approximation properties of complex-valued polynomial Trefftz spaces for the
(d+ 1)-dimensional linear time-dependent Schrödinger equation. More precisely, we prove …

A novel space-time discretization for the (linear) scalar-valued dissipative wave equation is
presented. It is a structured approach, namely, the discretization space is obtained …