Related papers: PatchworkWave: A Multipatch Infrastructure for Mul…
We present a "multipatch" infrastructure for numerical simulation of fluid problems in which sub-regions require different gridscales, different grid geometries, different physical equations, or different reference frames. Its key element…
We introduce Patchwork, a new general-purpose shape representation capable of modeling 2D and 3D geometry with a small number of parameters. Patchwork is grounded in a rigorous mathematical framework, providing provable complexity bounds…
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 describe a generic infrastructure for time evolution simulations in numerical relativity using multiple grid patches. After a motivation of this approach, we discuss the relative advantages of global and patch-local tensor bases. We…
Heliospheric plasmas require multi-scale and multi-physics considerations. On one hand, MHD codes are widely used for global simulations of the solar-terrestrial environments, but do not provide the most elaborate physical description of…
We introduce a high-performance simulation framework that permits the semi-independent, task-based solution of sets of partial differential equations, typically manifesting as updates to a collection of `patches' in space-time. A hybrid…
A key scalability challenge in neural solvers for industrial-scale physics simulations is efficiently capturing both fine-grained local interactions and long-range global dependencies across millions of spatial elements. We introduce the…
This article describes a new, fully adaptive Particle-Multiple-Mesh numerical simulation code developed primarily for simulations of small regions (such as a group of galaxies) in a cosmological context. It integrates the equations of…
In Robotics, especially in this era of autonomous driving, mapping is one key ability of a robot to be able to navigate through an environment, localize on it and analyze its traversability. To allow for real-time execution on constrained…
We propose a new computational framework that combines the recently developed time-parallel (TP) and the compound wavelet matrix (CWM) methods. The framework, termed tpCWM, offers significant computational acceleration by making…
Equation-free macroscale modelling is a systematic and rigorous computational methodology for efficiently predicting the dynamics of a microscale system at a desired macroscale system level. In this scheme, the given microscale model is…
In this work, we introduce a new Hybrid High-Order method for the numerical simulation of fracture propagation based on phase-field models. The proposed method supports general meshes made of polygonal/polyhedral elements, which provides…
The PMCHWT integral equation enables the modelling of scattering of time-harmonic fields by penetrable, piecewise homogeneous, systems. They have been generalised to include the modelling of composite systems that may contain junctions,…
The Equation-Free approach to efficient multiscale numerical computation marries trusted micro-scale simulations to a framework for numerical macro-scale reduction -- the patch dynamics scheme. A recent novel patch scheme empowered the…
Massive parallelisation has lead to a dramatic increase in available computational power. However, data transfer speeds have failed to keep pace and are the major limiting factor in the development of exascale computing. New algorithms must…
Scalable and efficient numerical simulations continue to gain importance, as computation is firmly established as the third pillar of discovery, alongside theory and experiment. Meanwhile, the performance of computing hardware grows through…
There is a class of problems that exhibit smooth behavior on macroscopic scales, where only a microscopic evolution law is known. Patch dynamics scheme of `equation-free multiscale modelling' is one of the techniques, which aims to extract…
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…
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…