Related papers: Efficient Exascale Discretizations: High-Order Fin…
An important step in shape optimization with partial differential equation constraints is to adapt the geometry during each optimization iteration. Common strategies are to employ mesh-deformation or re-meshing, where one or the other…
We present the derivation, implementation, and analysis of a multiresolution adaptive grid framework for numerical simulations on octree-based 3D block-structured collocated grids with distributed computational architectures. Our approach…
In addition to hardware wall-time restrictions commonly seen in high-performance computing systems, it is likely that future systems will also be constrained by energy budgets. In the present work, finite difference algorithms of varying…
The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated reassemblage of finite element matrices for nonlinear PDEs is…
This article introduces a general purpose framework and software to approximate partial differential equations (PDEs). The sparsity patterns of finite element discretized operators is identified automatically using the tools from…
Computing the stiffness matrix for the finite element discretization of the nonlocal Laplacian on unstructured meshes is difficult, because the operator is nonlocal and can even be singular. In this paper, we focus on the $C^0$-piecewise…
A new higher-order accurate method is proposed that combines the advantages of the classical $p$-version of the FEM on body-fitted meshes with embedded domain methods. A background mesh composed by higher-order Lagrange elements is used.…
Convex optimization over the spectrahedron, i.e., the set of all real $n\times n$ positive semidefinite matrices with unit trace, has important applications in machine learning, signal processing and statistics, mainly as a convex…
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…
We present a generic algorithm for numbering and then efficiently iterating over the data values attached to an extruded mesh. An extruded mesh is formed by replicating an existing mesh, assumed to be unstructured, to form layers of…
Efficient deep learning computing requires algorithm and hardware co-design to enable specialization: we usually need to change the algorithm to reduce memory footprint and improve energy efficiency. However, the extra degree of freedom…
We propose a new discretization method for PDEs on moving domains in the setting of unfitted finite element methods, which is provably higher-order accurate in space and time. In the considered setting, the physical domain that evolves…
Elliptic partial differential equations (PDEs) frequently arise in continuum descriptions of physical processes relevant to science and engineering. Multilevel preconditioners represent a family of scalable techniques for solving discrete…
Mixed dimensional partial differential equations (PDEs) are equations coupling unknown fields defined over domains of differing topological dimension. Such equations naturally arise in a wide range of scientific fields including geology,…
Collaborative edge computing (CEC) is an emerging paradigm where heterogeneous edge devices (stakeholders) collaborate to fulfill computation tasks, such as model training or video processing, by sharing communication and computation…
Accurate large-scale Kohn-Sham density functional theory (DFT) calculations are essential for modeling complex material systems, including interfaces, defects, nanoclusters, and twisted two-dimensional heterostructures. Achieving chemical…
Deep Ensembles are a simple, reliable, and effective method of improving both the predictive performance and uncertainty estimates of deep learning approaches. However, they are widely criticised as being computationally expensive, due to…
Implementing embedded neural network processing at the edge requires efficient hardware acceleration that couples high computational performance with low power consumption. Driven by the rapid evolution of network architectures and their…
Collaborative Edge Computing (CEC) is a new edge computing paradigm that enables neighboring edge servers to share computational resources with each other. Although CEC can enhance the utilization of computational resources, it still…
Given their increasing size and complexity, the need for efficient execution of deep neural networks has become increasingly pressing in the design of heterogeneous High-Performance Computing (HPC) and edge platforms, leading to a wide…