6 papers · 1 filter
Second-order invariant-domain preserving approximation to the multi-species Euler equations
Bennett Clayton, Tarik Dzanic, Eric J. Tovar
This work is concerned with constructing a second-order, invariant-domain preserving approximation of the compressible multi-species Euler equations where each species is modeled b…
A method for bounding high-order finite element functions: Applications to mesh validity and bounds-preserving limiters
Tarik Dzanic, Tzanio Kolev, Ketan Mittal
We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear boundi…
High-order limiting methods using maximum principle bounds derived from the Boltzmann equation I: Euler equations
Tarik Dzanic, Luigi Martinelli
The use of limiting methods for high-order numerical approximations of hyperbolic conservation laws generally requires defining an admissible region/bounds for the solution. In thi…
A note on higher-order and nonlinear limiting approaches for continuously bounds-preserving discontinuous Galerkin methods
Tarik Dzanic
In (Dzanic, J. Comp. Phys., 508:113010, 2024), a limiting approach for high-order discontinuous Galerkin schemes was introduced which allowed for imposing constraints on the soluti…
Continuously bounds-preserving discontinuous Galerkin methods for hyperbolic conservation laws
Tarik Dzanic
For finite element approximations of transport phenomena, it is often necessary to apply a form of limiting to ensure that the discrete solution remains well-behaved and satisfies…
DynAMO: Multi-agent reinforcement learning for dynamic anticipatory mesh optimization with applications to hyperbolic conservation laws
Tarik Dzanic, Ketan Mittal, Dohyun Kim +4
We introduce DynAMO, a reinforcement learning paradigm for Dynamic Anticipatory Mesh Optimization. Adaptive mesh refinement is an effective tool for optimizing computational cost a…