Related papers: Automatic Code Generation for High-Performance Dis…
Software design patterns are standard solutions to common problems in software design and architecture. Knowing that a particular module implements a design pattern is a shortcut to design comprehension. Manually detecting design patterns…
Numerical solution of nonlocal constrained value problems with integrable kernels are considered. These nonlocal problems arise in nonlocal mechanics and nonlocal diffusion. The structure of the true solution to the problem is analyzed…
The high-order accurate continuous Galerkin finite element method offers attractive computational efficiency for computational fluid dynamics. A challenge is however spurious oscillations which result for convection dominated flows over…
In this paper, we present a novel nodal integration scheme for meshfree Galerkin methods that draws on the mathematical framework of the virtual element method. We adopt linear maximum-entropy basis functions for the discretization of field…
Partial differential equations (PDEs) are crucial in modeling diverse phenomena across scientific disciplines, including seismic and medical imaging, computational fluid dynamics, image processing, and neural networks. Solving these PDEs at…
While large language models (LLMs) have been widely applied to code generation, they struggle with generating entire deep learning projects, which are characterized by complex structures, longer functions, and stronger reliance on domain…
We develop a high-order hybridized discontinuous Galerkin (HDG) method for a linear degenerate elliptic equation arising from a two-phase mixture of mantle convection or glacier dynamics. We show that the proposed HDG method is well-posed…
We propose a family of high-order local discontinuous Galerkin (LDG) methods, built on a parametric representation and coupled with a semi-implicit backward Euler time discretization, for isotropic and anisotropic curve-shortening flows.…
We consider a fully discretized numerical scheme for parabolic stochastic partial differential equations with multiplicative noise. Our abstract framework can be applied to formulate a non-iterative domain decomposition approach. Such…
When writing high-performance code for numerical computation in a scripting language like MATLAB, it is crucial to have the operations in a large for-loop vectorized. If not, the code becomes too slow to use, even for a moderately large…
Automated code generation is gaining significant importance in intelligent computer programming and system deployment. However, current approaches often face challenges in computational efficiency and lack robust mechanisms for code parsing…
SSE (streaming SIMD extensions) and AVX (advanced vector extensions) are SIMD (single instruction multiple data streams) instruction sets supported by recent CPUs manufactured in Intel and AMD. This SIMD programming allows parallel…
We introduce a new level-set shape optimization approach based on polytopic (i.e., polygonal in two and polyhedral in three spatial dimensions) discontinuous Galerkin methods. The approach benefits from the geometric mesh flexibility of…
In current computer architectures, data movement (from die to network) is by far the most energy consuming part of an algorithm (10pJ/word on-die to 10,000pJ/word on the network). To increase memory locality at the hardware level and reduce…
In convection-dominated flows, robustness of the spatial discretisation is a key property. While Interior Penalty Galerkin (IPG) methods already proved efficient in the situation of large mesh Peclet numbers, Arbitrary Lagrangian-Eulerian…
The rapid adoption of Large Language Models (LLMs) has transformed modern software development by enabling automated code generation at scale. While these systems improve productivity, they introduce new challenges for software governance,…
Unified visual grounding pursues a simple and generic technical route to leverage multi-task data with less task-specific design. The most advanced methods typically present boxes and masks as vertex sequences to model referring detection…
We present the latest developments of our High-Order Spectral Element Solver (HORSES3D), an open source high-order discontinuous Galerkin framework, capable of solving a variety of flow applications, including compressible flows (with or…
The long-time evolution of extreme mass-ratio inspiral systems requires minimal phase and dispersion errors to accurately compute far-field waveforms, while high accuracy is essential near the smaller black hole (modeled as a Dirac delta…
Spacetime Discontinuous Galerkin (DG) methods are used to solve hyperbolic PDEs describing wavelike physical phenomena. When the PDEs are nonlinear, the speed of propagation of the phenomena, called the wavespeed, at any point in the…