Related papers: A state redistribution algorithm for finite volume…
Embedded, or immersed, approaches have the goal of reducing to the minimum the computational costs associated with the generation of body-fitted meshes by only employing fixed, possibly Cartesian, meshes over which complex boundaries can…
We present a new algorithm for numerical magnetohydrodynamics on staggered meshes preserving $\nabla \cdot B = 0$. Our algorithm is based on the constrained transport method and supports both cell-based adaptive mesh refinement and temporal…
In this article we consider one-dimensional random systems of hyperbolic conservation laws. We first establish existence and uniqueness of random entropy admissible solutions for initial value problems of conservation laws which involve…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
Many probabilistic inference problems such as stochastic filtering or the computation of rare event probabilities require model analysis under initial and terminal constraints. We propose a solution to this bridging problem for the widely…
Towards the efficient simulation of near-term quantum devices using tensor network states, we introduce an improved real-space parallelizable matrix-product state (MPS) compression method. This method enables efficient compression of all…
In this work, we introduce new second-order schemes for one- and two-dimensional hyperbolic systems of conservation laws. Following an approach recently proposed in [{\sc R. Abgrall}, Commun. Appl. Math. Comput., 5 (2023), pp. 370--402], we…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
This paper studies the application of the blended dynamics approach towards distributed optimization problem where the global cost function is given by a sum of local cost functions. The benefits include (i) individual cost function need…
State estimation is key to both analyzing physical mechanisms and enabling real-time control of fluid flows. A common estimation approach is to relate sensor measurements to a reduced state governed by a reduced-order model (ROM). (When…
In this paper, we present a class of finite volume schemes for incompressible flow problems. The unknowns are collocated at the center of the control volumes, and the stability of the schemes is obtained by adding to the mass balance…
Time distributed optimization is an implementation strategy that can significantly reduce the computational burden of model predictive control by exploiting its robustness to incomplete optimization. When using this strategy, optimization…
Many applications involve partial differential equations which admits nontrivial steady state solutions. The design of schemes which are able to describe correctly these equilibrium states may be challenging for numerical methods, in…
This paper studies iterative schemes for measure transfer and approximation problems, which are defined through a slicing-and-matching procedure. Similar to the sliced Wasserstein distance, these schemes benefit from the availability of…
Gradient reconstruction is a key process for the spatial accuracy and robustness of finite volume method, especially in industrial aerodynamic applications in which grid quality affects reconstruction methods significantly. A novel gradient…
For conventional smoothed particle hydrodynamics (SPH), obtaining the static solution of a problem is time-consuming. To address this drawback, we propose an efficient dynamic relaxation method by adding large artificial-viscosity-based…
We apply the finite element cell-centered (FECC) scheme [2] to the solution of the nearly incompressible elasticity problem. By applying a technique of dual mesh, such a low-order finite element scheme can be constructed from any given mesh…
We present a novel distributionally robust framework for dynamic programming that uses kernel methods to design feedback control policies. Specifically, we leverage kernel mean embedding to map the transition probabilities governing the…
We propose a new parallel Discontinuous Galerkin method for the approximation of hyperbolic systems of conservation laws. The method remains stable with large time steps, while keeping the complexity of an explicit scheme: it does not…
We consider hyperbolic systems of conservation laws with relaxation source terms leading to a diffusive asymptotic limit under a parabolic scaling. We introduce a new class of secondorder in time and space numerical schemes, which are…