Related papers: General Field Evaluation in High-Order Meshes on G…
We present numerical experiments for geophysics electromagnetic (EM) modeling based upon high-order edge elements and supervised $h+p$ refinement approaches on massively parallel computers. Our high-order $h+p$ refinement strategy is based…
General Matrix Multiplication (GEMM) is a crucial algorithm for various applications such as machine learning and scientific computing, and an efficient GEMM implementation is essential for the performance of these systems. While…
3D models are widely used in various industries, and mesh data has become an indispensable part of 3D modeling because of its unique advantages. Mesh data can provide an intuitive and practical expression of rich 3D information. However,…
We develop a method for generating degree-of-freedom maps for arbitrary order finite element spaces for any cell shape. The approach is based on the composition of permutations and transformations by cell sub-entity. Current approaches to…
Local multiscale methods often construct multiscale basis functions in the offline stage without taking into account input parameters, such as source terms, boundary conditions, and so on. These basis functions are then used in the online…
Parametric feature grid encodings have gained significant attention as an encoding approach for neural fields since they allow for much smaller MLPs, which significantly decreases the inference time of the models. In this work, we propose…
Gaussian Process (GP) regression is a powerful nonparametric Bayesian framework, but its performance depends critically on the choice of covariance kernel. Selecting an appropriate kernel is therefore central to model quality, yet remains…
We present a mapping algorithm to compute large-scale magnetic field maps in indoor environments with approximate Gaussian process (GP) regression. Mapping the spatial variations in the ambient magnetic field can be used for localization…
Variational Gaussian process (GP) approximations have become a standard tool in fast GP inference. This technique requires a user to select variational features to increase efficiency. So far the common choices in the literature are…
This paper presents a mesh moving strategy for high-order Lagrangian method on quadrilateral meshes. The primary evidence of this method stems from principle of area conservative linearization and the asymptotic properties of the velocity.…
This paper addresses the problem of evaluating the quality of finite element meshes for the purpose of structural mechanic simulations. It proposes the application of a machine learning model trained on data collected from expert…
GPU-based heterogeneous architectures are now commonly used in HPC clusters. Due to their architectural simplicity specialized for data-level parallelism, GPUs can offer much higher computational throughput and memory bandwidth than CPUs in…
In this paper we propose and analyze a new Multiscale Method for solving semi-linear elliptic problems with heterogeneous and highly variable coefficient functions. For this purpose we construct a generalized finite element basis that spans…
An accurate implicit description of geometries is enabled by the level-set method. Level-set data is given at the nodes of a higher-order background mesh and the interpolated zero-level sets imply boundaries of the domain or interfaces…
As an alternative to classical numerical solvers for partial differential equations (PDEs) subject to boundary value constraints, there has been a surge of interest in investigating neural networks that can solve such problems efficiently.…
Only a few numerical methods can treat boundary value problems on polygonal and polyhedral meshes. The BEM-based Finite Element Method is one of the new discretization strategies, which make use of and benefits from the flexibility of these…
Explicit time advancement for continuous finite elements requires the inversion of a global mass matrix. For spectral element simulations on quadrilaterals and hexahedra, there is an accurate approximate mass matrix which is diagonal,…
As datasets grow it becomes infeasible to process them completely with a desired model. For giant datasets, we frame the order in which computation is performed as a decision problem. The order is designed so that partial computations are…
We devise a Hybrid High-Order (HHO) method for highly oscillatory elliptic problems that is capable of handling general meshes. The method hinges on discrete unknowns that are polynomials attached to the faces and cells of a coarse mesh;…
The matrix element method utilizes ab initio calculations of probability densities as powerful discriminants for processes of interest in experimental particle physics. The method has already been used successfully at previous and current…