Related papers: COFFEE: an Optimizing Compiler for Finite Element …
Information and communication technologies account for a growing portion of global environmental impacts. While emerging technologies, such as emerging non-volatile memories (eNVM), offer a promising solution to energy efficient computing,…
This work presents a reduced order modelling technique built on a high fidelity embedded mesh finite element method. Such methods, and in particular the CutFEM method, are attractive in the generation of projection-based reduced order…
The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE…
Specialized hardware accelerators are becoming important for more and more applications. Thanks to specialization, they can achieve high performance and energy efficiency but their design is complex and time consuming. This problem is…
This paper proposes a new parallel approach to solve connected components on a 2D binary image implemented with CUDA. We employ the following strategies to accelerate neighborhood exploration after dividing an input image into independent…
The Feynman-Kac formulae (FKF) express local solutions of partial differential equations (PDEs) as expectations with respect to some complementary stochastic differential equation (SDE). Repeatedly sampling paths from the complementary SDE…
Dataset condensation aims at reducing the network training effort through condensing a cumbersome training set into a compact synthetic one. State-of-the-art approaches largely rely on learning the synthetic data by matching the gradients…
A finite element method is presented to compute time harmonic microwave fields in three dimensional configurations. Nodal-based finite elements have been coupled with an absorbing boundary condition to solve open boundary problems. This…
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…
Finite element (FE) analysis has the potential to offset much of the expensive experimental testing currently required to certify aerospace laminates. However, large numbers of degrees of freedom are necessary to model entire aircraft…
Bringing high-level machine learning models to efficient and well-suited machine implementations often invokes a bunch of tools, e.g.~code generators, compilers, and optimizers. Along such tool chains, abstractions have to be applied. This…
In this paper, the generalized finite element method (GFEM) for solving second order elliptic equations with rough coefficients is studied. New optimal local approximation spaces for GFEMs based on local eigenvalue problems involving a…
Ensemble models are widely used to solve complex tasks by their decomposition into multiple simpler tasks, each one solved locally by a single member of the ensemble. Decoding of error-correction codes is a hard problem due to the curse of…
Training AI models that generalize across tasks and domains has long been among the open problems driving AI research. The emergence of Foundation Models made it easier to obtain expert models for a given task, but the heterogeneity of data…
We examine aspects of the computation of finite element matrices and vectors which are made possible by automated code generation. Given a variational form in a syntax which resembles standard mathematical notation, the low-level computer…
Advancements in Large Language Models (LLMs) have extended their input context length, yet they still struggle with retrieval and reasoning in long-context inputs. Existing methods propose to utilize the prompt strategy and retrieval head…
A key ingredient of our fictitious domain, higher order space-time cut finite element (CutFEM) approach for solving the incompressible Navier--Stokes equations on evolving domains (cf.\ \cite{Bause2021}) is the extension of the physical…
A novel method for performing model updating on finite element models is presented. The approach is particularly tailored to modal analyses of buildings, by which the lowest frequencies, obtained by using sensors and system identification…
High-level synthesis, source-to-source compilers, and various Design Space Exploration techniques for pragma insertion have significantly improved the Quality of Results of generated designs. These tools offer benefits such as reduced…
The paper introduces the development of a modular compiler for a subset of a C-like language, which addresses the challenges in constructing a compiler for high-level languages. This modular approach will allow developers to modify a…