Related papers: A new Dune grid for scalable dynamic adaptivity ba…
Numerical solvers of Partial Differential Equations (PDEs) are of fundamental significance to science and engineering. To date, the historical reliance on legacy techniques has circumscribed possible integration of big data knowledge and…
In this article, a new generic higher-order finite-element framework for massively parallel simulations is presented. The modular software architecture is carefully designed to exploit the resources of modern and future supercomputers.…
In this paper we describe generic algorithms and data structures for the implementation of $hp$-adaptive discontinuous finite element methods in the Dune-Fem library. Special attention is given to the often tedious and error-prone task of…
Computationally intensive algorithms such as Deep Neural Networks (DNNs) are becoming killer applications for edge devices. Porting heavily data-parallel algorithms on resource-constrained and battery-powered devices poses several…
In recent years, the use of artificial intelligence on resource-constrained IoT devices has grown significantly. However, existing approaches to DNN partitioning and offloading across the edge-cloud continuum typically rely on static…
Unstructured meshes present challenges in scientific data analysis due to irregular distribution and complex connectivity. Computing and storing connectivity information is a major bottleneck for visualization algorithms, affecting both…
We present an efficient MPI-parallel geometric multigrid library for quadtree (2D) or octree (3D) grids with adaptive refinement. Cartesian 2D/3D and cylindrical 2D geometries are supported, with second-order discretizations for the…
We tackle the challenge of detecting multiple change points in large time series by optimising a penalised likelihood derived from exponential family models. Dynamic programming algorithms can solve this task exactly with at most quadratic…
For the parallel computation of partial differential equations, one key is the grid partitioning. It requires that each process owns the same amount of computations, and also, the partitioning quality should be proper to reduce the…
The high computational demands of multiscale modeling necessitate advanced parallel and adaptive strategies. To address this challenge, we introduce an adaptive method that utilizes two microscale models based on an offline database for…
Second order accurate Cartesian grid methods have been well developed for interface problems in the literature. However, it is challenging to develop third or higher order accurate methods for problems with curved interfaces and internal…
Although recent scaling up approaches to training deep neural networks have proven to be effective, the computational intensity of large and complex models, as well as the availability of large-scale datasets, require deep learning…
In this work, we propose an adaptive geometric multigrid method for the solution of large-scale finite cell flow problems. The finite cell method seeks to circumvent the need for a boundary-conforming mesh through the embedding of the…
We present version 3 of the open-source simulator for flow and transport processes in porous media DuMu$^\text{x}$. DuMu$^\text{x}$ is based on the modular C++ framework Dune (Distributed and Unified Numerics Environment) and is developed…
In this work, we propose a novel adaptive grid mapping approach, the Adaptive Patched Grid Map, which enables a situational aware grid based perception for autonomous vehicles. Its structure allows a flexible representation of the…
Fault tolerant algorithms for the numerical approximation of elliptic partial differential equations on modern supercomputers play a more and more important role in the future design of exa-scale enabled iterative solvers. Here, we combine…
GPUs and other accelerators are increasingly used for scientific computing. In the future, we want to add GPU support to parallel adaptive mesh refinement (AMR) codes written in Fortran. To understand which changes are necessary to obtain…
Discovery Systems (DS) can be considered as entry points for global loosely coupled distributed systems. An efficient Discovery System in essence increases the performance, reliability and decision making capability of distributed systems.…
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…
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…