Related papers: Generating Finite Element Codes combining Adaptive…
The challenges associated with effectively programming FPGAs have been a major blocker in popularising reconfigurable architectures for HPC workloads. However new compiler technologies, such as MLIR, are providing new capabilities which…
Domain specific languages (DSLs) are increasingly used today. Coping with complex language definitions, evolving them in a structured way, and ensuring their error freeness are the main challenges of DSL design and implementation. The use…
We present a novel architecture for safely integrating Large Language Models (LLMs) into interactive game engines, allowing players to "program" new behaviors using natural language. Our framework mitigates risks by using an LLM to…
Multimodal systems, which process multiple input types such as text, audio, and images, are becoming increasingly prevalent in software systems, enabled by the huge advancements in Machine Learning. This triggers the need to easily define…
This paper addresses the problem of specifying and parsing the syntax of domain-specific languages (DSLs) in a modular, user-friendly way. That is, we want to enable the design of composable DSLs that combine the natural syntax of external…
This work introduces a novel, fully robust and highly-scalable, $h$-adaptive aggregated unfitted finite element method for large-scale interface elliptic problems. The new method is based on a recent distributed-memory implementation of the…
Recent developments show that Large Language Models (LLMs) produce state-of-the-art performance on natural language (NL) to code generation for resource-rich general-purpose languages like C++, Java, and Python. However, their practical…
The automated finite element analysis of complex CAD models using boundary-fitted meshes is rife with difficulties. Immersed finite element methods are intrinsically more robust but usually less accurate. In this work, we introduce an…
The ultimate goal of any numerical scheme for partial differential equations (PDEs) is to compute an approximation of user-prescribed accuracy at quasi-minimal computational time. To this end, algorithmically, the standard adaptive finite…
In today's rapidly evolving field of electronic design automation (EDA), the complexity of hardware designs is increasing, necessitating more sophisticated automation solutions. High-level synthesis (HLS), as a pivotal solution, automates…
This paper proposes a strategy to solve the problems of the conventional s-version of finite element method (SFEM) fundamentally. Because SFEM can reasonably model an analytical domain by superimposing meshes with different spatial…
Boundary element methods (BEM) reduce a partial differential equation in a domain to an integral equation on the domain's boundary. They are particularly attractive for solving problems on unbounded domains, but handling the dense matrices…
Large language models (LLMs) excel at generating code from natural language (NL) descriptions. However, the plain textual descriptions are inherently ambiguous and often fail to capture complex requirements like intricate system behaviors,…
Traditional compilers, designed for optimizing low-level code, fall short when dealing with modern, computation-heavy applications like image processing, machine learning, or numerical simulations. Optimizations should understand the…
The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). However, its mesh-based nature gives rise to substantial computational costs, especially for complex multiscale…
This work presents a polyhedral scaled boundary finite element method (PSBFEM) for three dimensional seepage analysis. We first derive the scaled boundary formulation for 3D seepage problems, and subsequently incorporate Wachspress shape…
Partial differential equations (PDEs) with inputs that depend on infinitely many parameters pose serious theoretical and computational challenges. Sophisticated numerical algorithms that automatically determine which parameters need to be…
In application domains that store data in a tabular format, a common task is to fill the values of some cells using values stored in other cells. For instance, such data completion tasks arise in the context of missing value imputation in…
In this paper, we develop an adaptive high-order surface finite element method (FEM) incorporating the spectral deferred correction method for chain contour discretization to solve polymeric self-consistent field equations on general curved…
We present the capabilities and results of the Parallel Edge-based Tool for Geophysical Electromagnetic modeling (PETGEM), as well as the physical and numerical foundations upon which it has been developed. PETGEM is an open-source and…