Related papers: Hamiltonian Simulation for Advection-Diffusion Equ…
We present an exact mathematical transformation which converts a wide class of advection-diffusion equations into a form allowing simple and direct spatial discretization in all dimensions, and thus the construction of accurate and more…
Two quantum algorithms are presented for the numerical solution of a linear one-dimensional advection-diffusion equation with periodic boundary conditions. Their accuracy and performance with increasing qubit number are compared…
Motivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we solve analytically a one-dimensional fractional diffusion-advection equation for the particle density. We…
The paper develops a hybrid method for solving a system of advection--diffusion equations in a bulk domain coupled to advection--diffusion equations on an embedded surface. A monotone nonlinear finite volume method for equations posed in…
This work proposes a novel shape optimization framework for geometric inverse problems governed by the advection--diffusion equation, based on the coupled complex boundary method (CCBM). Building on recent developments [Afr22, Rab23, Rab25,…
We describe an exact and highly efficient numerical algorithm for solving a special but important class of convection-diffusion equations. These equations occur in many problems in physics, chemistry, or biology, and they are usually hard…
Recently, Jin et al. proposed a quantum simulation technique for ANY linear partial differential equations (PDEs), called Schr\"{o}dingerisation [1,2,3]. In this paper, the Schr\"{o}dingerisation technique for quantum simulation is expanded…
This work addresses model order reduction for complex moving fronts, which are transported by advection or through a reaction-diffusion process. Such systems are especially challenging for model order reduction since the transport cannot be…
Quantum simulators were originally proposed for simulating one partial differential equation (PDE) in particular - Schrodinger's equation. Can quantum simulators also efficiently simulate other PDEs? While most computational methods for…
The extent to which quantum computers can simulate physical phenomena and solve the partial differential equations (PDEs) that govern them remains a central open question. In this work, one of the most fundamental PDEs is addressed: the…
Convection-diffusion equations provide the basis for describing heat and mass transfer phenomena as well as processes of continuum mechanics. To handle flows in porous media, the fundamental issue is to model correctly the convective…
Dynamical quantum simulation may be one of the first applications to see quantum advantage. However, the circuit depth of standard Trotterization methods can rapidly exceed the coherence time of noisy quantum computers. This has led to…
This article shows how to develop an efficient solver for a stabilized numerical space-time formulation of the advection-dominated diffusion transient equation. At the discrete space-time level, we approximate the solution by using…
Often computational models are too expensive to be solved in the entire domain of simulation, and a cheaper model would suffice away from the main zone of interest. We present for the concrete example of an evolution problem of advection…
Conventional approaches for simulating steady-state distributions of particles under diffusive and advective transport at high P\'eclet numbers involve solving the diffusion and advection equations in at least two dimensions. Here, we…
Quantum computing has emerged as a promising avenue for achieving significant speedup, particularly in large-scale PDE simulations, compared to classical computing. One of the main quantum approaches involves utilizing Hamiltonian…
A standard approach to solving the S$_N$ transport equations is to use source iteration with diffusion synthetic acceleration (DSA). Although this approach is widely used and effective on many problems, there remain some practical issues…
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…
This article studies a direct numerical approach for fractional advection-diffusion equations (ADEs). Using a set of cubic trigonometric B-splines as test functions, a differential quadrature (DQ) method is firstly proposed for the 1D and…
Many promising quantum applications depend on the efficient quantum simulation of an exponentially large sparse Hamiltonian, a task known as sparse Hamiltonian simulation, which is fundamentally important in quantum computation. Although…