Related papers: Streamline integration as a method for two-dimensi…

We present a simple numerical algorithm for solving elliptic equations where the diffusion coefficient, the source term, the solution and its flux are discontinuous across an irregular interface. The algorithm produces second-order accurate…

This paper introduces a novel geometric multigrid solver for unstructured curved surfaces. Multigrid methods are highly efficient iterative methods for solving systems of linear equations. Despite the success in solving problems defined on…

Second order accurate Cartesian grid methods have been well developed for interface problems in the literature. However, it is challenging to develop third or higher order accurate methods for problems with curved interfaces and internal…

We develop multilevel methods for interface-driven multiphysics problems that can be coupled across dimensions and where complexity and strength of the interface coupling deteriorates the performance of standard methods. We focus on solvers…

This paper deals with the discrete counterpart of 2D elliptic model problems rewritten in terms of Boundary Integral Equations. The study is done within the framework of Isogeometric Analysis based on B-splines. In such a context, the…

In this paper we propose a method for applications oriented input design for linear systems under time-domain constraints on the amplitude of input and output signals. The method guarantees a desired control performance for the estimated…

This paper proposes a novel heterogeneous grid convolution that builds a graph-based image representation by exploiting heterogeneity in the image content, enabling adaptive, efficient, and controllable computations in a convolutional…

The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…

Distribution grids include medium and low voltage lines that are involved in the delivery of electricity from substation to end-users/loads. A distribution grid is operated in a radial/tree-like structure, determined by switching on or off…

A new method SREAG (spherical rectangular equal-area grid) is proposed to divide a spherical surface into equal-area cells. The method is based on dividing a sphere into latitudinal rings of near-constant width with further splitting each…

Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate…

This paper presents a new column-and-constraint generation method for two-stage robust mixed-integer programs with finite uncertainty sets. Our method combines and extends speed-up techniques used in previous column-and-constraint…

In this paper, we propose and analyze a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. A complete convergence analysis is provided under the…

Central schemes are frequently used for incompressible and compressible flow calculations. The present paper is the first in a forthcoming series where a new approach to a 2nd order accurate Finite Volume scheme operating on cartesian grids…

Standard discretization techniques for boundary integral equations, e.g., the Galerkin boundary element method, lead to large densely populated matrices that require fast and efficient compression techniques like the fast multipole method…

Topological insulators show important properties, such as topological phase transitions and topological edge states. Although these properties and phenomena can be simulated by well-designed circuits, it is undoubtedly difficult to design…

We construct multigrid methods for an elliptic distributed optimal control problem that are robust with respect to a regularization parameter. We prove the uniform convergence of the $W$-cycle algorithm and demonstrate the performance of…

This paper describes a massively parallel algebraic multigrid method based on non-smoothed aggregation. It is especially suited for solving heterogeneous elliptic problems as it uses a greedy heuristic algorithm for the aggregation that…

We present a spectrally-accurate scheme to turn a boundary integral formulation for an elliptic PDE on a single unit cell geometry into one for the fully periodic problem. Applications include computing the effective permeability of…

This paper studies reduced-order modeling of dynamic networks with strongly connected topology. Given a graph clustering of an original complex network, we construct a quotient graph with less number of vertices, where the edge weights are…