Related papers: Matrix-Free Ghost Penalty Evaluation via Tensor Pr…
Unfitted finite element methods, like CutFEM, have traditionally been implemented in a matrix-based fashion, where a sparse matrix is assembled and later applied to vectors while solving the resulting linear system. With the goal of…
In this note, we develop a new stabilization mechanism for cut finite element methods that generalizes previous approaches of ghost penalty type in two ways: (1) The quantity that is stabilized and (2) The choice of elements that are…
This paper presents a matrix-free approach for implementing the shifted boundary method (SBM) in finite element analysis. The SBM is a versatile technique for solving partial differential equations on complex geometries by shifting boundary…
Recent hardware-aware matrix-free algorithms for higher-order finite-element (FE) discretized matrix-vector multiplications reduce floating point operations and data access costs compared to traditional sparse matrix approaches. This work…
In this work, we analyse the links between ghost penalty stabilisation and aggregation-based discrete extension operators for the numerical approximation of elliptic partial differential equations on unfitted meshes. We explore the behavior…
We present an algorithmic framework for matrix-free evaluation of discontinuous Galerkin finite element operators based on sum factorization on quadrilateral and hexahedral meshes. We identify a set of kernels for fast quadrature on cells…
Finite-element (FE) discretisations have emerged as a powerful real-space alternative to large-scale Kohn-Sham density functional theory (DFT) calculations, offering systematic convergence, excellent parallel scalability, while…
This paper presents a novel approach for solving fourth-order phase-field models in brittle fracture mechanics using the Interior Penalty Finite Element Method (IP-FEM). The fourth-order model improves numerical stability and accuracy…
We introduce the Fast Free Memory method (FFM), a new fast method for the numerical evaluation of convolution products. Inheriting from the Fast Multipole Method, the FFM is a descent-only and kernel-independent algorithm. We give the…
This study presents novel strategies for improving the node-level performance of matrix-free evaluation of continuous and discontinuous Galerkin spatial discretizations on unstructured tetrahedral grids. In our approach the underlying…
Several complex tasks that arise in organizations can be simplified by mapping them into a matrix completion problem. In this paper, we address a key challenge faced by our company: predicting the efficiency of artists in rendering visual…
The performance of finite element solvers on modern computer architectures is typically memory bound for sufficiently large problems. The main cause for this is that loading matrix elements from RAM into CPU cache is significantly slower…
We propose and analyze computationally a new fictitious domain method, based on higher order space-time finite element discretizations, for the simulation of the nonstationary, incompressible Navier-Stokes equations on evolving domains. The…
We introduce an unfitted Nitsche finite element method with a new ghost-penalty stabilization based on local projection of the solution gradient. The proposed ghost-penalty operator is straightforward to implement, ensures algebraic…
We develop and analyze a posteriori error estimators for a proper orthogonal decomposition-discrete empirical interpolation method (Pod-Deim) reduced order model applied to a parametric Poisson equation posed on a parameter-dependent domain…
This paper proposes a matrix-free residual evaluation technique for the hybridizable discontinuous Galerkin method requiring a number of operations scaling only linearly with the number of degrees of freedom. The method results from…
Tensor factorization models are widely used in many applied fields such as chemometrics, psychometrics, computer vision or communication networks. Real life data collection is often subject to errors, resulting in missing data. Here we…
The finite element method (FEM) has several computational steps to numerically solve a particular problem, to which many efforts have been directed to accelerate the solution stage of the linear system of equations. However, the finite…
We construct and analyze a CutFEM discretization for the Stokes problem based on the Scott-Vogelius pair. The discrete piecewise polynomial spaces are defined on macro-element triangulations which are not fitted to the smooth physical…
The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…