Thomas J. Radley
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View article: Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport
Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport Open
We introduce an hp -version discontinuous Galerkin finite element method (DGFEM) for the linear Boltzmann transport problem. A key feature of this new method is that, while offering arbitrary order convergence rates, it may be implemented …
View article: Quadrature-free polytopic discontinuous Galerkin methods for transport problems
Quadrature-free polytopic discontinuous Galerkin methods for transport problems Open
In this article we consider the application of Euler's homogeneous function theorem together with Stokes' theorem to exactly integrate families of polynomial spaces over general polygonal and polyhedral (polytopic) domains in two and three…
View article: Analysis of Iterative Methods for the Linear Boltzmann Transport Equation
Analysis of Iterative Methods for the Linear Boltzmann Transport Equation Open
In this article we consider the iterative solution of the linear system of equations arising from the discretisation of the poly-energetic linear Boltzmann transport equation using a discontinuous Galerkin finite element approximation in s…
View article: Quadrature-Free Polytopic Discontinuous Galerkin Methods for Transport Problems
Quadrature-Free Polytopic Discontinuous Galerkin Methods for Transport Problems Open
In this article we consider the application of Euler's homogeneous function theorem together with Stokes' theorem to exactly integrate families of polynomial spaces over general polygonal and polyhedral (polytopic) domains in two- and thre…
View article: Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport
Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport Open
We introduce an $hp$-version discontinuous Galerkin finite element method (DGFEM) for the linear Boltzmann transport problem. A key feature of this new method is that, while offering arbitrary order convergence rates, it may be implemented…
View article: Moving mesh methods for implicit moving boundary problems
Moving mesh methods for implicit moving boundary problems Open
Numerical algorithms for implicit moving boundary problems require the ability to predict both the evolution of the boundary and the dynamics of the solution in the interior.When these dynamics are governed by partial differential equation…