Related papers: Automated MPI-X code generation for scalable finit…
We consider adaptive finite element methods for solving a multiscale system consisting of a macroscale model comprising a system of reaction-diffusion partial differential equations coupled to a microscale model comprising a system of…
We present a simple and easy to apply methodology for using high-level self-submitting parallel job queues in an MPI environment. Using C++, we implemented a library of functions, MPQueue, both for testing our concepts and for use in real…
This paper introduces madupite, a high-performance distributed solver for large-scale Markov Decision Processes (MDPs). MDPs are widely used to model complex dynamical systems in various fields, including finance, epidemiology, and traffic…
Heterogeneous systems are becoming more common on High Performance Computing (HPC) systems. Even using tools like CUDA and OpenCL it is a non-trivial task to obtain optimal performance on the GPU. Approaches to simplifying this task include…
State of the art domain decomposition algorithms for large-scale boundary value problems (with $M\gg 1$ degrees of freedom) suffer from bounded strong scalability because they involve the synchronisation and communication of workers…
The study deals with the parallelization of 2D and 3D finite element based Navier-Stokes codes using direct solvers. Development of sparse direct solvers using multifrontal solvers has significantly reduced the computational time of direct…
Deep code generation is a topic of deep learning for software engineering (DL4SE), which adopts neural models to generate code for the intended functions. Since end-to-end neural methods lack domain knowledge and software hierarchy…
We present Decapodes, a diagrammatic tool for representing, composing, and solving partial differential equations. Decapodes provides an intuitive diagrammatic representation of the relationships between variables in a system of equations,…
Exact diagonalization is a well-established method for simulating small quantum systems. Its applicability is limited by the exponential growth of the so-called Hamiltonian matrix that needs to be diagonalized. Physical symmetries are…
Partial differential equations (PDEs) with near singular solutions pose significant challenges for traditional numerical methods, particularly in complex geometries where mesh generation and adaptive refinement become computationally…
We present a computational method for extreme-scale simulations of incompressible turbulent wall flows at high Reynolds numbers. The numerical algorithm extends a popular method for solving second-order finite differences Poisson/Helmholtz…
Recent work has suggested using Monte Carlo methods based on piecewise deterministic Markov processes (PDMPs) to sample from target distributions of interest. PDMPs are non-reversible continuous-time processes endowed with momentum, and…
The code generation capabilities of Large Language Models (LLMs) have advanced applications like tool invocation and problem-solving. However, improving performance in code-related tasks remains challenging due to limited training data that…
There has been rapid progress recently on the application of deep networks to the solution of partial differential equations, collectively labelled as Physics Informed Neural Networks (PINNs). In this paper, we develop Physics Informed…
MPI's derived datatypes (DDTs) promise easier, copy-free communication of non-contiguous data, yet their practical performance remains debated and is often reported only for a single MPI stack. We present a cross-implementation assessment…
We introduce suitable coordinate systems for pipes and their variants that allow us to transform partial differential equations (PDEs) on the pipe surfaces or in the solid pipes into computational domains with fixed limits/ranges. Such a…
Traditional numerical techniques for solving time-dependent partial-differential-equation (PDE) initial-value problems (IVPs) store a truncated representation of the function values and some number of their time derivatives at each time…
This paper introduces a new approach to generating sample paths of unknown Markovian stochastic differential equations (SDEs) using diffusion models, a class of generative AI methods commonly employed in image and video applications. Unlike…
A new method for solving numerically stochastic partial differential equations (SPDEs) with multiple scales is presented. The method combines a spectral method with the heterogeneous multiscale method (HMM) presented in [W. E, D. Liu, and…
Partial differential equations (PDEs) are ubiquitous in the world around us, modelling phenomena from heat and sound to quantum systems. Recent advances in deep learning have resulted in the development of powerful neural solvers; however,…