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Elliptic partial differential equations (PDEs) can model many physical phenomena, such as electrostatics, acoustics, wave propagation, and diffusion. In scientific machine learning settings, a high-throughput PDE solver …

We present a new framework for the fast solution of inhomogeneous elliptic boundary value problems in domains with smooth boundaries. High-order solvers based on adaptive box codes …

Machine learning based surrogate models offer researchers powerful tools for accelerating simulation-based workflows. However, as standard datasets in this space often cover small classes of physical behavior …

We introduce a fast direct solver for variable-coefficient elliptic PDEs on surfaces based on the hierarchical Poincaré–Steklov method. The method takes as input an unstructured, high …

Polynomial spectral methods provide fast, accurate, and flexible solvers for broad ranges of PDEs with one bounded dimension, where the incorporation of general boundary conditions is well understood …

How does breaking the symmetry of an equation alter the symmetry of its solutions? Here, we systematically examine how reducing underlying symmetries from spherical to axisymmetric influences the …

Reaction-diffusion models with nonlocal constraints naturally arise as limiting cases of coupled bulk-surface models of intracellular signalling. In this paper, a minimal, mass-conserving model of …