相关论文: Higher order accuracy in the gap-tooth scheme for …
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 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 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,…
An important class of problems exhibits macroscopically smooth behaviour in space and time, while only a microscopic evolution law is known. For such time-dependent multi-scale problems, the gap-tooth scheme has recently been proposed. The…
Preserving scalar boundedness is important for numerical schemes used in turbulent compressible multi-component flow simulations to prevent unphysical results and unstable simulations. However, ensuring scalar boundedness for high-order,…
This note reports on a scheme for interpolating the boundary conditions be- tween non-adjacent modeling regions when the model is based on Monte-Carlo computations of a collection of particles. The scheme conserves particles in a natural…
In this paper, we propose high order numerical methods to solve a 2D advection diffusion equation, in the highly oscillatory regime. We use an integrator strategy that allows the construction of arbitrary high-order schemes {leading} to an…
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…
A novel approach for simulating potential propagation in neuronal branches with high accuracy is developed. The method relies on high-order accurate difference schemes using the Summation-By-Parts operators with weak boundary and interface…
The need to smoothly cover a computational domain of interest generically requires the adoption of several grids. To solve the problem of interest under this grid-structure one must ensure the suitable transfer of information among the…
The multiscale patch scheme is built from given small micro-scale simulations of complicated physical processes to empower large macro-scale simulations. By coupling small patches of simulations over unsimulated spatial gaps, large savings…
Scientists and engineers often create accurate, trustworthy, computational simulation schemes - but all too often these are too computationally expensive to execute over the time or spatial domain of interest. The equation-free approach is…
We construct new, efficient, and accurate high-order finite differencing operators which satisfy summation by parts. Since these operators are not uniquely defined, we consider several optimization criteria: minimizing the bandwidth, the…
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…
A single-step high-order implicit time integration scheme with controllable numerical dissipation at high frequencies is presented for the transient analysis of structural dynamic problems. The amount of numerical dissipation is controlled…
We describe high order accurate and stable finite difference schemes for the initial-boundary value problem associated with the magnetic induction equations. These equations model the evolution of a magnetic field due to a given velocity…
We present a higher-order boundary condition for atomistic simulations of dislocations that address the slow convergence of standard supercell methods. The method is based on a multipole expansion of the equilibrium displacement, combining…
Exponential integrators based on contour integral representations lead to powerful numerical solvers for a variety of ODEs, PDEs, and other time-evolution equations. They are embarrassingly parallelizable and lead to global-in-time…
We present a high-order method that provides numerical integration on volumes, surfaces, and lines defined implicitly by two smooth intersecting level sets. To approximate the integrals, the method maps quadrature rules defined on…