Related papers: A two-scale approach for efficient on-the-fly oper…
The computational complexity of naive, sampling-based uncertainty quantification for 3D partial differential equations is extremely high. Multilevel approaches, such as multilevel Monte Carlo (MLMC), can reduce the complexity significantly,…
We extend a distributed finite element method built upon model order reduction to arbitrary polynomial degree using a hybrid Nitsche scheme. The new method considerably simplifies the transformation of the finite element system to the…
Architectures with multiple classes of memory media are becoming a common part of mainstream supercomputer deployments. So called multi-level memories offer differing characteristics for each memory component including variation in…
We develop a sparse multiscale operator-adapted wavelet decomposition-based finite element method (FEM) on unstructured polygonal mesh hierarchies obtained via a coarsening procedure. Our approach decouples different resolution levels,…
We present a new meshless method for scalar diffusion equations which is motivated by their compatible discretizations on primal-dual grids. Unlike the latter though, our approach is truly meshless because it only requires the graph of…
We describe an efficient algorithm for computing the matrix vector products that appear in the numerical resolution of boundary integral equations in 2 space dimension. This work is an extension of the so-called Sparse Cardinal Sine…
We present multigrid methods for solving elliptic partial differential equations on arbitrary domains using the nodal ghost finite element method, an unfitted boundary approach where the domain is implicitly defined by a level-set function.…
A general method for accelerating fixed point schemes for problems related to partial differential equations is presented in this article. The speedup is obtained by training a reduced-order model on-the-fly, removing the need to do an…
Algebraic Multigrid (AMG) methods are state-of-the-art algebraic solvers for partial differential equations. Still, their efficiency depends heavily on the choice of suitable parameters and/or ingredients. Paradigmatic examples include the…
The automated finite element analysis of complex CAD models using boundary-fitted meshes is rife with difficulties. Immersed finite element methods are intrinsically more robust but usually less accurate. In this work, we introduce an…
This work presents a novel methodology for speeding up the assembly of stiffness matrices for laminate composite 3D structures in the context of isogeometric and finite element discretizations. By splitting the involved terms into their…
Plane arrangements are a useful tool for surface and volume modelling. However, their main drawback is poor scalability. We introduce two key novelties that enable the construction of plane arrangements for complex objects and entire…
A hypergraph ${\cal F}$ is a set family defined on vertex set $V$. The dual of ${\cal F}$ is the set of minimal subsets $H$ of $V$ such that $F\cap H \ne \emptyset$ for any $F\in {\cal F}$. The computation of the dual is equivalent to many…
Chordal and factor-width decomposition methods for semidefinite programming and polynomial optimization have recently enabled the analysis and control of large-scale linear systems and medium-scale nonlinear systems. Chordal decomposition…
In contrast with many other convex optimization classes, state-of-the-art semidefinite programming solvers are yet unable to efficiently solve large scale instances. This work aims to reduce this scalability gap by proposing a novel…
Stencil computation is an important class of scientific applications that can be efficiently executed by graphics processing units (GPUs). Out-of-core approach helps run large scale stencil codes that process data with sizes larger than the…
Modeling complex spatial networks with multiscale heterogeneity poses significant mathematical and computational challenges. Lacking explicit PDE discretizations and facing excessive degrees of freedom, conventional methods often become…
Solving high-dimensional partial differential equations (PDEs) efficiently requires handling multi-scale features across varying resolutions. To address this challenge, we present the Multiwavelet-based Multigrid Neural Operator (M2NO), a…
Optimal control problems with nonsmooth objectives and nonlinear partial differential equation (PDE) constraints are challenging, mainly because of the underlying nonsmooth and nonconvex structures and the demanding computational cost for…
We consider the primal and dual forms of the optimality conditions for PDE-contrained optimization problems arising in Data-Driven Computational Mechanics when specialized to the reaction-diffusion context. Starting with the continuous…