Related papers: A versatile FEM framework with native GPU scalabil…
Adaptive Computing is an application-agnostic outer loop framework to strategically deploy simulations and experiments to guide decision making for scale-up analysis. Resources are allocated over successive batches, which makes the…
This project aims to advance differentiable fluid dynamics for hypersonic coupled flow over porous media, demonstrating the potential of automatic differentiation (AD)-based optimization for end-to-end solutions. Leveraging AD efficiently…
Modern vision models achieve remarkable accuracy, but explaining where evidence arises, what the model encodes, and how internal computations assemble that evidence remains fragmented. We introduce an iERF-centric framework that unifies…
Fracture produces new mesh fragments that introduce additional degrees of freedom in the system dynamics. Existing finite element method (FEM) based solutions suffer from an explosion in computational cost as the system matrix size…
In this work, we develop a neural-physics solver based on finite volume method (FVM), namely NeuralFVM, for turbulent flows by implementing the standard $k$-$\omega$ model designed for efficient Graphics Processing Unit (GPU) execution. The…
We present and analyze a linearized finite element method (FEM) for the dynamical incompressible magnetohydrodynamics (MHD) equations. The finite element approximation is based on mixed conforming elements, where Taylor--Hood type elements…
This paper proposes some efficient and accurate adaptive two-grid (ATG) finite element algorithms for linear and nonlinear partial differential equations (PDEs). The main idea of these algorithms is to utilize the solutions on the $k$-th…
Designing effective optimisation strategies for unsteady flows in the presence of complex dynamics is challenging. Gradient-based optimisation algorithms that rely on gradient information obtained from adjoint equations are efficient for…
The $hp$-adaptive finite element method (FEM) - where one independently chooses the mesh size ($h$) and polynomial degree ($p$) to be used on each cell - has long been known to have better theoretical convergence properties than either $h$-…
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…
Differentiable programming, enabled by automatic differentiation (AD), provides a robust framework for gradient-based optimization in computational plasma physics. While optimization is often only used towards design, we demonstrate that it…
We present cudaclaw, a CUDA-based high performance data-parallel framework for the solution of multidimensional hyperbolic partial differential equation (PDE) systems, equations describing wave motion. cudaclaw allows computational…
Edge computing facilitates deep learning in resource-constrained environments, but challenges such as resource heterogeneity and dynamic constraints persist. This paper introduces AMP4EC, an Adaptive Model Partitioning framework designed to…
In this paper, we develop the constraint energy minimization generalized multiscale finite element method (CEM-GMsFEM) in mixed formulation applied to parabolic equations with heterogeneous diffusion coefficients. The construction of the…
We present a framework for solving a broad class of ill-posed inverse problems governed by partial differential equations (PDEs), where the target coefficients of the forward operator are recovered through an iterative regularization scheme…
This chapter provides an overview of state-of-the-art adaptive finite element methods (AFEMs) for the numerical solution of second-order elliptic partial differential equations (PDEs), where the primary focus is on the optimal interplay of…
We present a simple variational framework for planar elastica that enables distributed energies, such as gravitational loading or magnetic body torques, to be incorporated in a modular and unified manner. The formulation is based on…
This paper introduces a Variational Multiscale Stabilization (VMS) formulation of the incompressible Navier--Stokes equations that utilizes the Finite Element Exterior Calculus (FEEC) framework. The FEEC framework preserves the geometric…
We propose an energy-stable parametric finite element method (ES-PFEM) to discretize the motion of a closed curve under surface diffusion with an anisotropic surface energy $\gamma(\theta)$ -- anisotropic surface diffusion -- in two…
Maxwell's equations are a system of partial differential equations that govern the laws of electromagnetic induction. We study a mimetic finite-difference (MFD) discretization of the equations which preserves important underlying physical…