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The recently proposed Hamiltonian Adaptive Resolution Scheme (H-AdResS) allows to perform molecular simulations in an open boundary framework. It allows to change on the fly the resolution of specific subset of molecules (usually the…
We present the development and benchmarking of Poisson solvers for graphics processing units (GPUs). Implemented in the Astaroth platform, the solvers feature high computational efficiency. We present novel combinations of discretizations…
Recently, a lot of papers proposed to use neural networks to approximately solve partial differential equations (PDEs). Yet, there has been a lack of flexible framework for convenient experimentation. In an attempt to fill the gap, we…
A projection-based immersed boundary method is dominated by sparse linear algebra routines. Using the open-source Cusp library, we observe a speedup (with respect to a single CPU core) which reflects the constraints of a bandwidth-dominated…
This paper presents a lightweight, open-source and high-performance python package for solving peridynamics problems in solid mechanics. The development of this solver is motivated by the need for fast analysis tools to achieve the large…
It is well known since 1960s that by exploring the tensor product structure of the discrete Laplacian on Cartesian meshes, one can develop a simple direct Poisson solver with an $\mathcal O(N^{\frac{d+1}d})$ complexity in d-dimension, where…
Elliptic partial differential equations arise in many fields of science and engineering such as steady state distribution of heat, fluid dynamics, structural/mechanical engineering, aerospace engineering and seismology etc. In three…
We introduce CuPyMag, an open-source, Python-based framework for large-scale micromagnetic simulations with magnetostriction. CuPyMag solves micromagnetics with finite elements in a GPU-resident workflow in which key operations, such as…
An explicit solution of the stationary one dimensional half-space boundary value problem for the linear Boltzmann equation is presented in the presence of an arbitrarily high constant external field. The collision kernel is assumed to be…
We show how to accelerate the direct solution of the Boltzmann equation using Graphics Processing Units (GPUs). In order to fully exploit the computational power of the GPU, we choose a method of solution which combines a finite difference…
The phase field method is an effective tool for modeling microstructure evolution in materials. Many efficient implicit numerical solvers have been proposed for phase field simulations under uniform and time-invariant model parameters. We…
Particle breakage due to collisional interactions plays a vital role in the development of several phenomena in science and engineering. The nonlinear collisional breakage equations (NCBEs) are a significant set of equations in this…
In the present paper, a fluid-particle coupling method is directly derived from the Navier-Stokes equations (NSE) by applying the concept of volume-filtering, yielding a physically consistent methodology to incorporate solid wall boundary…
Under the most common experimental conditions, the adsorption of proteins to solid surfaces is an spontaneous process that leads to a rather compact layer of randomly oriented molecules. Due to the importance of this process for the…
Cell blebs are protrusions of the cell membrane and can be instrumental for cell migration. We derive a continuum model for the mechanical and geometrical aspects of the onset of blebbing in terms of a force balance. It is abstract and…
The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet for fluid problems it only achieves first-order spatial accuracy near embedded boundaries for the velocity field and…
The singularities that arise in elliptic boundary value problems are treated locally by a singular function boundary integral method. This method extracts the leading singular coefficients from a series expansion that describes the local…
This paper describes the main features of a pioneering unsteady solver for simulating ideal two-fluid plasmas on unstructured grids, taking profit of GPGPU (General-purpose computing on graphics processing units). The code, which has been…
We consider the preconditioned conjugate gradient method (PCG) with optimal preconditioner in the frame of the boundary element method (BEM) for elliptic first-kind integral equations. Our adaptive algorithm steers the termination of PCG as…