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Improving sampling efficacy on high dimensional distributions with thin high density regions using Conservative Hamiltonian Monte Carlo
Geoffrey McGregor, Andy T. S. Wan
Hamiltonian Monte Carlo is a prominent Markov Chain Monte Carlo algorithm, which employs symplectic integrators to sample from high dimensional target distributions in many applica…
Parametric Interpolation Framework for 1-D Scalar Conservation Laws with Non-Convex Flux Functions
Geoffrey McGregor, Jean-Christophe Nave
In this paper we present a novel framework for obtaining high order numerical methods for 1-D scalar conservation laws with non-convex flux functions. When solving Riemann problems…
Parametric Interpolation Framework for Scalar Conservation Laws
Geoffrey McGregor, Jean-Christophe Nave
In this paper we present a novel framework for obtaining high-order numerical methods for scalar conservation laws in one-space dimension for both the homogeneous and non-homogeneo…
Area-Preserving Geometric Hermite Interpolation
Geoffrey McGregor, Jean-Christophe Nave
In this paper we establish a framework for planar geometric interpolation with exact area preservation using cubic Bézier polynomials. We show there exists a family of such curves…
A Parametric Interpolation Framework for 1D Scalar Conservation Laws using the Equal Area Principle
Geoffrey McGregor, Jean-Christophe Nave
In this paper we develop a novel framework for numerically solving scalar conservation laws in one space dimension. Utilizing the method of characteristics in conjunction with the…