Related papers: Generating Finite Element Codes combining Adaptive…
Many texts, especially in chemistry and biology, describe complex processes. We focus on texts that describe a chemical reaction process and questions that ask about the process's outcome under different environmental conditions. To answer…
In this work we formally derive and prove the correctness of the algorithms and data structures in a parallel, distributed-memory, generic finite element framework that supports h-adaptivity on computational domains represented as…
Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…
We consider the reliable implementation of high-order unfitted finite element methods on Cartesian meshes with hanging nodes for elliptic interface problems. We construct a reliable algorithm to merge small interface elements with their…
We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…
Over the past decade, different domain-specific languages (DSLs) were proposed to formally specify requirements stated in legal contracts, mainly for analysis but also for code generation. Symboleo is a promising language in that area.…
This article presents a new Domain Specific Embedded Language (DSEL) dedicated to Software-Defined Radio (SDR). From a set of carefully designed components, it enables to build efficient software digital communication systems, able to take…
This paper presents a DSL for geometric relations between rigid bodies such as relative position, orientation, pose, linear velocity, angular velocity, and twist. The DSL is the formal model of the recently proposed semantics for the…
A higher-order accurate finite element method is proposed which uses automatically generated meshes based on implicit level-set data for the description of boundaries and interfaces in two and three dimensions. The method is an alternative…
The advent of large language models (LLMs) has significantly advanced artificial intelligence (AI) in software engineering (SE), with source code embeddings playing a crucial role in tasks such as source code clone detection and source code…
Code completion is a prominent application of Large Language Models (LLMs) in software engineering. Due to the near real-time response requirements of this task, base models with small to medium-sized parameters are typically employed,…
We present 2-D, 3-D, and spherical mesh generators for the Finite Element Method (FEM) using triangular and tetrahedral elements. The mesh nodes are treated as if they were linked by virtual springs that obey Hooke's law. Given the desired…
Multiple scale homogenization problems are reduced to single scale problems in higher dimension. It is shown that sparse tensor product Finite Element Methods (FEM) allow the numerical solution in complexity independent of the dimension and…
We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness…
While Large Language Models (LLMs) have significantly advanced code generation efficiency, they face inherent challenges in balancing performance and inference costs across diverse programming tasks. Dynamically selecting the optimal LLM…
Deep models have achieved impressive progress in solving partial differential equations (PDEs). A burgeoning paradigm is learning neural operators to approximate the input-output mappings of PDEs. While previous deep models have explored…
Automated front-end engineering drastically reduces development cycles and minimizes manual coding overhead. While Generative AI has shown promise in translating designs to code, current solutions often produce monolithic scripts, failing…
In this paper, we present a new immersed finite element scheme for solving elliptic interface problems on unfitted meshes by combining the skeletal finite element method (FEM) with the standard FEM. The skeletal FEM is used for the…
Large language models (LLMs) have significantly improved code generation, particularly in one-pass code generation. However, most existing approaches focus solely on generating code in a single programming language, overlooking the…
We consider a general nonsymmetric second-order linear elliptic PDE in the framework of the Lax-Milgram lemma. We formulate and analyze an adaptive finite element algorithm with arbitrary polynomial degree that steers the adaptive…