Related papers: A multi-physics compiler for generating numerical …
A new OpenFOAM application to simulate multiphase flows in porous media is formulated and tested. The proposed solver combines the Eulerian multi-fluid formulation for a system of phase fractions with Darcy's law for flows through porous…
Deep learning-based molecular generation models have shown great potential in efficiently exploring vast chemical spaces by generating potential drug candidates with desired properties. However, these models often produce chemically invalid…
A rigorous asymptotic analysis of the Boltzmann equation for small Knudsen numbers leads, in the general case, to more complicated sets of differential equations than widely used to describe the behavior of gas in terms of classical fluid…
We present a flexible scalable open-source computational framework, named SECUReFoam, based on the finite-volume library OpenFOAM(R), for flow and transport problems in highly heterogeneous geological media and other porous materials. The…
Simulation is a foundational tool for the analysis and testing of cyber-physical systems (CPS), underpinning activities such as algorithm development, runtime monitoring, and system verification. As CPS grow in complexity and scale,…
Optimization time integrators are effective at solving complex multi-physics problems including deformable solids with non-linear material models, contact with friction, strain limiting, etc. For challenging problems, Newton-type optimizers…
This work develops a multiscale solution decomposition (MSD) method for nonlocal-in-time problems to separate a series of known terms with multiscale singularity from the original singular solution such that the remaining unknown part…
Closed-form differential equations, including partial differential equations and higher-order ordinary differential equations, are one of the most important tools used by scientists to model and better understand natural phenomena.…
As the Science Mission Directorate contemplates establishing an open code policy, we consider it timely to share our experiences as the developers of the open-source partial differential equation solver Dedalus. Dedalus is a flexible…
OpenSBLI is an open-source code-generation system for compressible fluid dynamics (CFD) on heterogeneous computing architectures. Written in Python, OpenSBLI is an explicit high-order finite-difference solver on structured curvilinear…
In this work, we present scalable balancing domain decomposition by constraints methods for linear systems arising from arbitrary order edge finite element discretizations of multi-material and heterogeneous 3D problems. In order to enforce…
Time-dependent partial differential equations are a significant class of equations that describe the evolution of various physical phenomena over time. One of the open problems in scientific computing is predicting the behaviour of the…
The phase-field method has become a useful tool for the simulation of classical metallurgical phase transformations as well as other phenomena related to materials science. The thermodynamic consistency that forms the basis of these…
The Finite Difference Time Domain (FDTD) method is a widely used numerical technique for solving Maxwell's equations, particularly in computational electromagnetics and photonics. It enables accurate modeling of wave propagation in complex…
Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm…
The combination of machine learning and physical laws has shown immense potential for solving scientific problems driven by partial differential equations (PDEs) with the promise of fast inference, zero-shot generalisation, and the ability…
Different possible sources are discussed for enhancement of the calculation time when solving ordinary differential equations systems to forecast space objects' motion. This paper presents an approach for building an integrator of ordinary…
We present an end-to-end framework to learn partial differential equations that brings together initial data production, selection of boundary conditions, and the use of physics-informed neural operators to solve partial differential…
Differentiable simulators continue to push the state of the art across a range of domains including computational physics, robotics, and machine learning. Their main value is the ability to compute gradients of physical processes, which…
Differentiable physics is a powerful tool in computer vision and robotics for scene understanding and reasoning about interactions. Existing approaches have frequently been limited to objects with simple shape or shapes that are known in…