Related papers: Simulation of percolation on massively-parallel co…
We present an algorithm for cluster dynamics to efficiently simulate large systems on MIMD parallel computers with large numbers of processors. The method divides physical space into rectangular cells which are assigned to processors and…
Realistic simulations in engineering or in the materials sciences can consume enormous computing resources and thus require the use of massively parallel supercomputers. The probability of a failure increases both with the runtime and with…
A new homogenization approach for the simulation of multi-phase flows in heterogeneous porous media is presented. It is based on the lattice Boltzmann method and combines the grayscale with the multi-component Shan-Chen method. Thus, it…
For massive data stored at multiple machines, we propose a distributed subsampling procedure for the composite quantile regression. By establishing the consistency and asymptotic normality of the composite quantile regression estimator from…
Based on the worm algorithm in the path-integral representation, we propose a general quantum Monte Carlo algorithm suitable for parallelizing on a distributed-memory computer by domain decomposition. Of particular importance is its…
Multiscale and inhomogeneous molecular systems are challenging topics in the field of molecular simulation. In particular, modeling biological systems in the context of multiscale simulations and exploring material properties are driving a…
We present the submatrix method, a highly parallelizable method for the approximate calculation of inverse p-th roots of large sparse symmetric matrices which are required in different scientific applications. We follow the idea of…
We develop a version of Mikhalkin's lattice path algorithm for projective hypersurfaces of arbitrary degree and dimension, which enumerates singular tropical hypersurfaces passing through appropriate configuration of points. By proving a…
Simulation of the monodomain equation, crucial for modeling the heart's electrical activity, faces scalability limits when traditional numerical methods only parallelize in space. To optimize the use of large multi-processor computers by…
Particle tracking in large-scale numerical simulations of turbulent flows presents one of the major bottlenecks in parallel performance and scaling efficiency. Here, we describe a particle tracking algorithm for large-scale parallel…
An efficient algorithm is constructed for contracting two-dimensional tensor networks under periodic boundary conditions. The central ingredient is a novel renormalization step that scales linearly with system size, i.e. from $L \to L+1$.…
In recent years there has been a considerable drive towards data-driven analysis, discovery and control of dynamical systems. To this end, operator theoretic methods, namely, Koopman operator methods have gained a lot of interest. In…
High-dimensional partial-differential equations (PDEs) arise in a number of fields of science and engineering, where they are used to describe the evolution of joint probability functions. Their examples include the Boltzmann and…
Relaxation processes driven by a Laplacian matrix can be found in many real-world big-data systems, for example, in search engines on the World-Wide-Web and the dynamic load balancing protocols in mesh networks. To numerically implement…
We present new algorithms for the parallelization of Eulerian-Lagrangian interaction operations in the immersed boundary method. Our algorithms rely on two well-studied parallel primitives: key-value sort and segmented reduce. The use of…
In view of the existing limitations of sequential computing, parallelization has emerged as an alternative in order to improve the speedup of numerical simulations. In the framework of evolutionary problems, space-time parallel methods…
We propose a new parallel Discontinuous Galerkin method for the approximation of hyperbolic systems of conservation laws. The method remains stable with large time steps, while keeping the complexity of an explicit scheme: it does not…
With the rapid growth of large language models (LLMs), a wide range of methods have been developed to distribute computation and memory across hardware devices for efficient training and inference. While existing surveys provide descriptive…
We introduce a Monte Carlo method, as a modification of existing cluster algorithms, which allows simulations directly on systems of infinite size, and for quantum models also at beta=infinity. All two-point functions can be obtained,…
The two-layer computer simulators are commonly used to mimic multi-physics phenomena or systems. Usually, the outputs of the first-layer simulator (also called the inner simulator) are partial inputs of the second-layer simulator (also…