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Three-dimensional rigid-body transforms, i.e. rotations and translations, are central to modern differentiable machine learning pipelines in robotics, vision, and simulation. However, numerically robust and mathematically correct…

Machine Learning · Computer Science 2025-11-27 Martin Schuck , Alexander von Rohr , Angela P. Schoellig

This article introduces a general purpose framework and software to approximate partial differential equations (PDEs). The sparsity patterns of finite element discretized operators is identified automatically using the tools from…

Numerical Analysis · Mathematics 2024-10-17 Kiefer Green , Harbir Antil

The implementation of efficient multigrid preconditioners for elliptic partial differential equations (PDEs) is a challenge due to the complexity of the resulting algorithms and corresponding computer code. For sophisticated finite element…

Mathematical Software · Computer Science 2016-10-07 Lawrence Mitchell , Eike Hermann Müller

This work is a user guide to the FEMPAR scientific software library. FEMPAR is an open-source object-oriented framework for the simulation of partial differential equations (PDEs) using finite element methods on distributed-memory…

Mathematical Software · Computer Science 2019-11-26 Santiago Badia , Alberto F. Martín

Domain-specific high-productivity environments are playing an increasingly important role in scientific computing due to the levels of abstraction and automation they provide. In this paper we introduce Devito, an open-source…

Mathematical Software · Computer Science 2017-07-13 Michael Lange , Navjot Kukreja , Fabio Luporini , Mathias Louboutin , Charles Yount , Jan Hückelheim , Gerard J. Gorman

Physics-Informed Neural Networks (PINN) has evolved into a powerful tool for solving partial differential equations, which has been applied to various fields such as energy, environment, en-gineering, etc. When utilizing PINN to solve…

Fluid Dynamics · Physics 2024-11-27 Zijie Su , Yunpu Liu , Sheng Pan , Zheng Li , Changyu Shen

A state-of-the-art deep domain decomposition method (D3M) based on the variational principle is proposed for partial differential equations (PDEs). The solution of PDEs can be formulated as the solution of a constrained optimization…

Machine Learning · Computer Science 2020-04-03 Ke Li , Kejun Tang , Tianfan Wu , Qifeng Liao

Optimization on manifolds is a class of methods for optimization of an objective function, subject to constraints which are smooth, in the sense that the set of points which satisfy the constraints admits the structure of a differentiable…

Mathematical Software · Computer Science 2020-09-03 James Townsend , Niklas Koep , Sebastian Weichwald

We present the theory, algorithms and implementation of a parallel finite-volume algorithm for the solution of the incompressible magnetohydrodynamic (MHD) equations using unstructured grids that are applicable for a wide variety of…

Fluid Dynamics · Physics 2016-01-11 S. Vantieghem , A. Sheyko , A. Jackson

{\sc ParMooN} is a program package for the numerical solution of elliptic and parabolic partial differential equations. It inherits the distinct features of its predecessor {\sc MooNMD} \cite{JM04}: strict decoupling of geometry and finite…

Applications in science and engineering often require huge computational resources for solving problems within a reasonable time frame. Parallel supercomputers provide the computational infrastructure for solving such problems. A…

Distributed, Parallel, and Cluster Computing · Computer Science 2007-05-23 Rajesh Sudarsan , Calvin J. Ribbens

Partial Differential Equations (PDEs) are fundamental tools for modeling physical phenomena, yet most PDEs of practical interest cannot be solved analytically and require numerical approximations. The feasibility of such numerical methods,…

Numerical Analysis · Mathematics 2025-12-03 Juan Esteban Suarez Cardona , Holger Boche , Gitta Kutyniok

Matrix Distributed Processing (MDP) is a C++ library for fast development of efficient parallel algorithms. It constitues the core of FermiQCD. MDP enables programmers to focus on algorithms, while parallelization is dealt with…

High Energy Physics - Lattice · Physics 2007-05-23 Massimo Di Pierro

We present an object-oriented open-source framework for solving the dynamics of open quantum systems written in Python. Arbitrary Hamiltonians, including time-dependent systems, may be built up from operators and states defined by a quantum…

Quantum Physics · Physics 2012-04-27 J. R. Johansson , P. D. Nation , Franco Nori

The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…

Numerical Analysis · Mathematics 2021-06-15 Cale Harnish , Luke Dalessandro , Karel Matous , Daniel Livescu

Solving partial differential equations (PDE) is an indispensable part of many branches of science as many processes can be modelled in terms of PDEs. However, recent numerical solvers require manual discretization of the underlying equation…

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…

Instrumentation and Methods for Astrophysics · Physics 2018-03-21 Å. Nordlund , J. P. Ramsey , A. Popovas , M. Kuffmeier

Molecular dynamics simulations play an increasingly important role in the rational design of (nano)-materials and in the study of biomacromolecules. However, generating input files and realistic starting coordinates for these simulations is…

Numerical solution of partial differential equations on parallel computers using domain decomposition usually requires synchronization and communication among the processors. These operations often have a significant overhead in terms of…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-01-11 Soumyadip Ghosh , Jiacai Lu , Vijay Gupta , Gretar Tryggvason