Related papers: Generating Finite Element Codes combining Adaptive…
Automatic code synthesis from natural language descriptions is a challenging task. We witness massive progress in developing code generation systems for domain-specific languages (DSLs) employing sequence-to-sequence deep learning…
The Finite Element Method (FEM) is widely used to solve discrete Partial Differential Equations (PDEs) in engineering and graphics applications. The popularity of FEM led to the development of a large family of variants, most of which…
We present a new finite element method, called $\phi$-FEM, to solve numerically elliptic partial differential equations with natural (Neumann or Robin) boundary conditions using simple computational grids, not fitted to the boundary of the…
Generation of software from modeling languages such as UML and domain specific languages (DSLs) has become an important paradigm in software engineering. In this contribution, we present some positions on software development in a model…
Efficiently and accurately simulating partial differential equations (PDEs) in and around arbitrarily defined geometries, especially with high levels of adaptivity, has significant implications for different application domains. A key…
DSLs and hardware accelerators have proven to be very effective in optimizing computationally expensive workloads. In this paper, we propose a solution to the challenge of manually rewriting legacy or unoptimized code in domain-specific…
We propose a finite-element local basis-based operator learning framework for solving partial differential equations (PDEs). Operator learning aims to approximate mappings from input functions to output functions, where the latter are…
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…
We propose an adaptive iteratively linearized finite element method (AILFEM) in the context of strongly monotone nonlinear operators in Hilbert spaces. The approach combines adaptive mesh-refinement with an energy-contractive linearization…
(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…
This work introduces an innovative parallel, fully-distributed finite element framework for growing geometries and its application to metal additive manufacturing. It is well-known that virtual part design and qualification in additive…
New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side).…
We study the generalized finite element methods (GFEMs) for the second-order elliptic eigenvalue problem with an interface in 1D. The linear stable generalized finite element methods (SGFEM) were recently developed for the elliptic source…
We consider a linear symmetric and elliptic PDE and a linear goal functional. We design and analyze a goal-oriented adaptive finite element method, which steers the adaptive mesh-refinement as well as the approximate solution of the arising…
Finite differences, finite elements, and their generalizations are widely used for solving partial differential equations, and their high-order variants have respective advantages and disadvantages. Traditionally, these methods are treated…
FPGA-based graph processing accelerators, enabling extensive customization, have demonstrated significant energy efficiency over general computing engines like CPUs and GPUs. Nonetheless, customizing accelerators to diverse graph processing…
There is currently a large amount of robotics software using the component-oriented programming paradigm. However, the rapid growth in number and complexity of components may compromise the scalability and the whole lifecycle of robotics…
Background:Technical systems are growing in complexity with more components and functions across various disciplines. Model-Driven Engineering (MDE) helps manage this complexity by using models as key artifacts. Domain-Specific Languages…
Inverse problems for Partial Differential Equations (PDEs) are crucial in numerous applications such as geophysics, biomedical imaging, and material science, where unknown physical properties must be inferred from indirect measurements. In…
We explore a new way to handle flux boundary conditions imposed on level sets. The proposed approach is a diffuse interface version of the shifted boundary method (SBM) for continuous Galerkin discretizations of conservation laws in…