Related papers: Asynchronous Discrete Event Schemes for PDEs
The application of Stochastic Differential Equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we…
We are interested in the discretisation of a drift-diffusion system in the framework of hybrid finite volume (HFV) methods on general polygonal/polyhedral meshes. The system under study is composed of two anisotropic and nonlinear…
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…
Stochastic differential equations (SDEs) provide a natural framework for modelling intrinsic stochasticity inherent in many continuous-time physical processes. When such processes are observed in multiple individuals or experimental units,…
A time-domain numerical modeling of transversely isotropic Biot poroelastic waves is proposed in two dimensions. The viscous dissipation occurring in the pores is described using the dynamic permeability model developed by…
This paper considers the optimal boundary control of chemical systems described by advection-diffusion-reaction (ADR) equations. We use a discontinuous Galerkin finite element method (DG-FEM) for the spatial discretization of the governing…
Transport processes are ubiquitous. They are, for example, at the heart of optical flow approaches; or of perfusion imaging, where blood transport is assessed, most commonly by injecting a tracer. An advection-diffusion equation is widely…
In this work we develop implicit Active Flux schemes for the scalar advection equation. At every cell interface we approximate the solution by a polynomial in time. This allows to evolve the point values using characteristics and to update…
We propose a second order exponential scheme suitable for two-component coupled systems of stiff evolutionary advection--diffusion--reaction equations in two and three space dimensions. It is based on a directional splitting of the involved…
We introduce a general framework for solving partial differential equations (PDEs) using generative diffusion models. In particular, we focus on the scenarios where we do not have the full knowledge of the scene necessary to apply classical…
This paper presents a finite volume method for simulating two-phase flows using a level set approach coupled with volume of fluid method capable of simulating sharp fluid interfaces. The efficiency of the method is a result of the fact that…
The convergence of a family of AMF-Runge-Kutta methods (in short AMF-RK) for the time integration of evolutionary Partial Differential Equations (PDEs) of Advection Diffusion Reaction type semi-discretized in space is considered. The…
This paper proposes a systematic and explicit quantum circuit framework for solving advection-diffusion equations with boundary conditions, based on the Linear Combination of Hamiltonian Simulations (LCHS) method. By employing the Finite…
We demonstrate a method for filtering images defined on curved surfaces embedded in 3D. Applications are noise removal and the creation of artistic effects. Our approach relies on in-surface diffusion: we formulate Weickert's edge/coherence…
We prove convergence of discrete duality finite volume (DDFV) schemes on distorted meshes for a class of simplified macroscopic bidomain models of the electrical activity in the heart. Both time-implicit and linearised time-implicit schemes…
Recent learning-based methods for event-based optical flow estimation utilize cost volumes for pixel matching but suffer from redundant computations and limited scalability to higher resolutions for flow refinement. In this work, we take…
Complex multidimensional stochastic dynamics can be approximately described as diffusion along reaction coordinates (RCs). If the RCs are optimally selected, the diffusive model allows one to compute important properties of the dynamics…
Common techniques for the spatial discretisation of PDEs on a macroscale grid include finite difference, finite elements and finite volume methods. Such methods typically impose assumed microscale structures on the subgrid fields, so…
We develop a framework for constructing mixed multiscale finite volume methods for elliptic equations with multiple scales arising from flows in porous media. Some of the methods developed using the framework are already known…
We introduce a new Eulerian simulation framework for liquid animation that leverages both finite element and finite volume methods. In contrast to previous methods where the whole simulation domain is discretized either using the finite…