Related papers: PCPATCH: software for the topological construction…
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…
Two new relaxation schemes are proposed for the smoothing step in the geometric multigrid solution of PDEs on 2D and 3D stretched structured grids. The new schemes are characterized by efficient line relaxation on branched sets of lines of…
We present a "multipatch" infrastructure for numerical simulation of fluid problems in which sub-regions require different gridscales, different grid geometries, different physical equations, or different reference frames. Its key element…
The accurate assembly of the system matrix is an important step in any code that solves partial differential equations on a mesh. We either explicitly set up a matrix, or we work in a matrix-free environment where we have to be able to…
Vertex-patch smoothers are essential for the robust convergence of geometric multigrid methods in high-order finite element applications, yet their adoption is traditionally hindered by the prohibitive cost of solving local patch problems.…
Fully realizing the potential of multigrid solvers often requires custom algorithms for a given application model, discretizations and even regimes of interest, despite considerable effort from the applied math community to develop fully…
Isogeometric Analysis is a high-order discretization method for boundary value problems that uses a number of degrees of freedom which is as small as for a low-order method. Standard isogeometric discretizations require a global…
In recent publications, the author and his coworkers have shown robust approximation error estimates for B-splines of maximum smoothness and have proposed multigrid methods based on them. These methods allow to solve the linear system…
The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…
Semidefinite programming (SDP) is widely acknowledged as one of the most effective methods for deriving the tightest lower bounds of the optimal power flow (OPF) problems. In this paper, an enhanced semidefinite relaxation model that…
We present and analyze a preconditioned conjugate gradient method (PCG) for solving spatial network problems. Primarily, we consider diffusion and structural mechanics simulations for fiber based materials, but the methodology can be…
Multiple patterning lithography has been widely adopted in advanced technology nodes of VLSI manufacturing. As a key step in the design flow, multiple patterning layout decomposition (MPLD) is critical to design closure. Due to the…
Patch-based relaxation refers to a family of methods for solving linear systems which partitions the matrix into smaller pieces often corresponding to groups of adjacent degrees of freedom residing within patches of the computational…
In this paper, we consider the problem of partitioning a polygon into a set of connected disjoint sub-polygons, each of which covers an area of a specific size. The work is motivated by terrain covering applications in robotics, where the…
Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…
Computational methods are driving high impact microscopy techniques such as ptychography. However, the design and implementation of new algorithms is often a laborious process, as many parts of the code are written in close-to-the-hardware…
In recent years, topology optimization has been developed sufficiently and many researchers have concentrated on enhancing to computationally numerical algorithms for computational effectiveness of this method. Along with the development of…
Semidefinite Programming (SDP) provides tight lower bounds for Optimal Power Flow problems. However, solving large-scale SDP problems requires exploiting sparsity. In this paper, we experiment several clique decomposition algorithms that…
We propose a novel method to fit and segment multi-structural data via convex relaxation. Unlike greedy methods --which maximise the number of inliers-- this approach efficiently searches for a soft assignment of points to models by…
Within recent years, considerable progress has been made regarding high-performance solvers for Partial Differential Equations (PDEs), yielding potential gains in efficiency compared to industry standard tools. However, the latter largely…