Related papers: Damping factors for the gap-tooth scheme
An important class of problems exhibits smooth behaviour in space and time on a macroscopic scale, while only a microscopic evolution law is known. For such time-dependent multi-scale problems, an ``equation-free framework'' has been…
We explore the gap-tooth method for multiscale modeling of systems represented by microscopic physics-based simulators, when coarse-grained evolution equations are not available in closed form. A biased random walk particle simulation,…
The multiscale gap-tooth scheme is built from given microscale simulations of complicated physical processes to empower macroscale simulations. By coupling small patches of simulations over unsimulated physical gaps, large savings in…
An important class of problems exhibits smooth behaviour on macroscopic space and time scales, while only a microscopic evolution law is known. For such time-dependent multi-scale problems, an "equation-free" framework has been proposed, of…
We are developing a framework for multiscale computation which enables models at a ``microscopic'' level of description, for example Lattice Boltzmann, Monte Carlo or Molecular Dynamics simulators, to perform modelling tasks at the…
The multiscale gap-tooth scheme uses a given microscale simulator of complicated physical processes to enable macroscale simulations by computing only only small sparse patches. This article develops the gap-tooth scheme to the case of…
Many astrophysical simulations involve extreme dynamic range of timescales around 'special points' in the domain (e.g. black holes, stars, planets, disks, galaxies, shocks, mixing interfaces), where processes on small scales couple strongly…
We propose and analyse numerical schemes for a system of quasilinear, degenerate evolution equations modelling biofilm growth as well as other processes such as flow through porous media and the spreading of wildfires. The first equation in…
One possibility for avoiding constraint violation in numerical relativity simulations adopting free-evolution schemes is to modify the continuum evolution equations so that constraint violations are damped away. Gundlach et. al.…
We are developing a framework for multiscale computation which enables models at a ``microscopic'' level of description, for example Lattice Boltzmann, Monte Carlo or Molecular Dynamics simulators, to perform modelling tasks at…
Recent developments in multiscale computation allow the solution of ``coarse equations'' for the expected macroscopic behavior of microscopically/stochastically evolving particle distributions without ever obtaining these coarse equations…
We introduce a general formulation for an implicit equation-free method in the setting of slow-fast systems. First, we give a rigorous convergence result for equation-free analysis showing that the implicitly defined coarse-level time…
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…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
Suitable gauge conditions are fundamental for stable and accurate numerical-relativity simulations of inspiralling compact binaries. A number of well-studied conditions have been developed over the last decade for both the lapse and the…
The implicit compact finite-difference scheme was developed for evolutionary partial differential parabolic and Schr\"odinger-type equations and systems with a weak nonlinearity. To make a temporal step of the compact implicit scheme we…
Over the past few decades, there has been substantial interest in evolution equations that involving a fractional-order derivative of order $\alpha\in(0,1)$ in time, due to their many successful applications in engineering, physics, biology…
Finite difference schemes, using Backward Differentiation Formula (BDF), are studied for the approximation of one-dimensional diffusion equations with an obstacle term, of the form $$\min(v_t - a(t,x) v_{xx} + b(t,x) v_x + r(t,x) v, v-…
Subspace learning and matrix factorization problems have great many applications in science and engineering, and efficient algorithms are critical as dataset sizes continue to grow. Many relevant problem formulations are non-convex, and in…
Real-time decoding plays a crucial role in practical fault-tolerant quantum computing. Window decoding, in which the decoding problem is divided into windows, is a promising approach. While reducing the window size is desirable for faster…