Related papers: A Holomorphic Embedding Based Continuation Method …
This paper presents a generalization to image matching of the Hamiltonian approach for planar curve matching developed in the context of group of diffeomorphisms. We propose an efficient framework to deal with discontinuous images in any…
We present a homotopic approach to solving challenging, optimization-based motion planning problems. The approach uses Homotopy Optimization, which, unlike standard continuation methods for solving homotopy problems, solves a sequence of…
In this paper, we present the derivation of a multicontinuum model for the coupled flow and transport equations by applying multicontinuum homogenization. We perform the multicontinuum expansion for both flow and transport solutions and…
The goal of load balancing (grid partitioning) is to minimize overall computations and communications, and to make sure that all processors have a similar workload. Geometric methods divide a grid by using a location of a cell while…
We present a particle method for estimating the curvature of interfaces in volume-of-fluid simulations of multiphase flows. The method is well suited for under-resolved interfaces, and it is shown to be more accurate than the parabolic…
This paper introduces a fast Central Processing Unit (CPU) implementation of geodesic morphological operations using stream processing. In contrast to the current state-of-the-art, that focuses on achieving insensitivity to the filter sizes…
The non-Euclidean geometry of hyperbolic spaces has recently garnered considerable attention in the realm of representation learning. Current endeavors in hyperbolic representation largely presuppose that the underlying hierarchies can be…
In this paper, we propose a local model reduction approach for subsurface flow problems in stochastic and highly heterogeneous media. To guarantee the mass conservation, we consider the mixed formulation of the flow problem and aim to solve…
We consider the problem of tracking one solution path defined by a polynomial homotopy on a parallel shared memory computer. Our robust path tracker applies Newton's method on power series to locate the closest singular parameter value. On…
In this article, we introduce a new homotopy function to trace the trajectory by applying modified homotopy continuation method for finding the solution of the linear complementarity problem. Earlier several authors attempted to propose…
We consider the coupled system of equations that describe flow in fractured porous media. To describe such types of problems, multicontinuum and multiscale approaches are used. Because in multicontinuum models, the permeability of each…
We introduce a new technique to visualize complex flowing phenomena by using concepts from shape analysis. Our approach uses techniques that examine the intrinsic geometry of manifolds through their heat kernel, to obtain representations of…
High-fidelity simulations of unsteady fluid flow are now possible with advancements in high-performance computing hardware and software frameworks. Since computational fluid dynamics (CFD) computations are dominated by linear algebraic…
Hamilton's equations are fundamental for modeling complex physical systems, where preserving key properties such as energy and momentum is crucial for reliable long-term simulations. Geometric integrators are widely used for this purpose,…
Simulating charged many-body systems has been a computational demanding task due to the long-range nature of electrostatic interaction. For the multi-scale model of electrolytes which combines the strengths of atomistic/continuum…
In this paper, we present two multidimensional power flow formulations based on a fixed-point iteration (FPI) algorithm to efficiently solve hundreds of thousands of power flows in distribution systems. The presented algorithms are the base…
In this article, we consider nonlinear complementarity problem. We introduce a new homotopy function for finding the solution of nonlinear complementarity problem through the trajectory . We show that the homotopy path approaching the…
A high-performance gas kinetic solver using multi-level parallelization is developed to enable pore-scale simulations of rarefied flows in porous media. The Boltzmann model equation is solved by the discrete velocity method with an…
The AC power flow equations describe the steady-state behavior of the power grid. While many algorithms have been developed to compute solutions to the power flow equations, few theoretical results are available characterizing when such…
We present an approach to construct appropriate and efficient emulators for Hamiltonian flow maps. Intended future applications are long-term tracing of fast charged particles in accelerators and magnetic plasma confinement configurations.…