Related papers: PCPATCH: software for the topological construction…
In this paper, we present a novel general framework grounded in the factor graph theory to solve kinematic and dynamic problems for multi-body systems. Although the motion of multi-body systems is considered to be a well-studied problem and…
We present a Python package called Modular Petri Net Assembly Toolkit (MPAT) that empowers users to easily create large-scale, modular Petri Nets for various spatial configurations, including extensive spatial grids or those derived from…
We consider geometric multigrid methods for the solution of linear systems arising from isogeometric discretizations of elliptic partial differential equations. For classical finite elements, such methods are well known to be fast solvers…
The present work develops hybrid multigrid methods for high-order discontinuous Galerkin discretizations of elliptic problems. Fast matrix-free operator evaluation on tensor product elements is used to devise a computationally efficient PDE…
We present a geometric multigrid solver for the Compact Discontinuous Galerkin method through building a hierarchy of coarser meshes using a simple agglomeration method which handles arbitrary element shapes and dimensions. The method is…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
We present a new framework for expressing finite element methods on multiple intersecting meshes: multimesh finite element methods. The framework enables the use of separate meshes to discretize parts of a computational domain that are…
Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP…
In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques…
In this work we study convex relaxations of quadratic optimisation problems over permutation matrices. While existing semidefinite programming approaches can achieve remarkably tight relaxations, they have the strong disadvantage that they…
Uni- and bivariate data smoothing with spline functions is a well established method in nonparametric regression analysis. The extension to multivariate data is straightforward, but suffers from exponentially increasing memory and…
During the last decade, Neural Networks (NNs) have proved to be extremely effective tools in many fields of engineering, including autonomous vehicles, medical diagnosis and search engines, and even in art creation. Indeed, NNs often…
This paper introduces a novel approach to algebraic multigrid methods for large systems of linear equations coming from finite element discretizations of certain elliptic second order partial differential equations. Based on a discrete…
Despite recent progress, recovering parametric CAD construction sequences from geometric input, such as meshes or point clouds, is a key challenge for design and manufacturing, as existing CAD reconstruction and generation methods are…
Semidefinite relaxations are widely used to compute upper bounds on the objective of optimization problems involving noncommutative polynomials. Such optimization problems are prevalent in quantum information. We present an algorithm able…
In practice, non-specialized interior point algorithms often cannot utilize the massively parallel compute resources offered by modern many- and multi-core compute platforms. However, efficient distributed solution techniques are required,…
A recent cutting-edge topic in multimodal modeling is to unify visual comprehension and generation within a single model. However, the two tasks demand mismatched decoding regimes and visual representations, making it non-trivial to jointly…
In solving hard computational problems, semidefinite program (SDP) relaxations often play an important role because they come with a guarantee of optimality. Here, we focus on a popular semidefinite relaxation of K-means clustering which…
This paper studies exact semidefinite programming relaxations (SDPRs) for separable quadratically constrained quadratic programs (QCQPs). We consider the construction of a larger separable QCQP from multiple QCQPs with exact SDPRs. We show…
A method is presented to include irregular domain boundaries in a geometric multigrid solver. Dirichlet boundary conditions can be imposed on an irregular boundary defined by a level set function. Our implementation employs quadtree/octree…