A5057121475- Numerical methods in engineering
- Advanced Numerical Methods in Computational Mathematics
- Matrix Theory and Algorithms
- Electromagnetic Simulation and Numerical Methods
- Geotechnical Engineering and Underground Structures
- Advanced Mathematical Modeling in Engineering
- Numerical methods for differential equations
- Model Reduction and Neural Networks
- Electromagnetic Scattering and Analysis
- Computational Fluid Dynamics and Aerodynamics
- Advanced Memory and Neural Computing
- Probabilistic and Robust Engineering Design
- Microstructure and mechanical properties
- Tensor decomposition and applications
- Advanced Optimization Algorithms Research
- Ferroelectric and Negative Capacitance Devices
- Parallel Computing and Optimization Techniques
- Neural Networks and Applications
- Fractional Differential Equations Solutions
- Fluid Dynamics and Turbulent Flows
- Medical Image Segmentation Techniques
- Optical measurement and interference techniques
- Advanced Vision and Imaging
- Neural Networks and Reservoir Computing
- Image Processing Techniques and Applications
Sandia National Laboratories California
2013-2024
Sandia National Laboratories
2015-2024
Tulane University
2022
Florida State University
2004-2010
National Technical Information Service
2006-2009
Office of Scientific and Technical Information
2008-2009
Applied Mathematics (United States)
2007-2009
Computer Algorithms for Medicine
2007-2008
Los Alamos National Laboratory
2002
Oak Ridge National Laboratory
2001
The Trilinos Project is an effort to facilitate the design, development, integration, and ongoing support of mathematical software libraries within object-oriented framework for solution large-scale, complex multiphysics engineering scientific problems. addresses two fundamental issues developing these problems: (i) providing a streamlined process set tools development new algorithmic implementations (ii) promoting interoperability independently developed software.Trilinos uses two-level...
A deflation procedure is introduced that designed to improve the convergence of an implicitly restarted Arnoldi iteration for computing a few eigenvalues large matrix. As progresses, Ritz value approximations converge at different rates. numerically stable scheme deflates converged from iteration. We present two forms implicit deflation. The first, locking operation, decouples values and associated vectors active part second, purging removes unwanted but pairs. Convergence improved reduction...
A recently developed nonlocal vector calculus is exploited to provide a variational analysis for general class of diffusion problems described by linear integral equation on bounded domains in $\mbRn$. The also enables striking analogies be drawn between the model and classical models diffusion, including notion flux. ubiquity operator applications illustrated number examples ranging from continuum mechanics graph theory. In particular, it shown that fractional Laplacian derivative anomalous...
A vector calculus for nonlocal operators is developed, including the definition of divergence, gradient, and curl derivation corresponding adjoint operators. Nonlocal analogs several theorems identities differential are also presented. Relationships between their counterparts established, first in a distributional sense then weak by considering weighted integrals The used to define volume-constrained problems that analogous elliptic boundary-value operators; this demonstrated via some...
The paper presents an overview of peridynamics, a continuum theory that employs nonlocal model force interaction. Specifically, the stress/strain relationship classical elasticity is replaced by integral operator sums internal forces separated finite distance. This not function deformation gradient, allowing for more general notion than in well aligned with kinematic assumptions molecular dynamics. Peridynamics effectiveness has been demonstrated several applications, including fracture and...
We develop a calculus for nonlocal operators that mimics Gauss's theorem and Green's identities of the classical vector calculus. The we define do not involve derivatives. then apply to weak formulations “boundary-value” problems mimic Dirichlet Neumann second-order scalar elliptic partial differential equations. For problems, derive fundamental solution functions, demonstrate are well posed, show how, under appropriate limits, reduce their local analogues.
We present an automated multilevel substructuring (AMLS) method for eigenvalue computations in linear elastodynamics a variational and algebraic setting. AMLS first recursively partitions the domain of PDE into hierarchy subdomains. Then generates subspace approximating eigenvectors associated with smallest eigenvalues by computing partial eigensolutions subdomains interfaces between them. remark that although we elastodynamics, our formulation is abstract applies to generic H1 -elliptic...
This paper considers the finite element approximation and algebraic solution of pure Neumann problem. Our goal is to present a concise variational framework for problem that focuses on interplay between problems. While many results stem from our analysis are known by some experts, they seldom derived in rigorous fashion remain part numerical folklore. As result, this knowledge not accessible (or appreciated) practitioners---both novices experts---in one source. contributes simple, yet...
Peridynamics is a formulation of continuum mechanics based on integral equations. It nonlocal model, accounting for the effects long-range forces. Correspondingly, classical molecular dynamics also model. and have similar discrete computational structures, as peridynamics computes force particle by summing forces from surrounding particles, similarly to dynamics. We demonstrate that model can be cast an upscaling Specifically, we address extent which solutions simulations recovered...
Anasazi is a package within the Trilinos software project that provides framework for iterative, numerical solution of large-scale eigenvalue problems. written in ANSI C++ and exploits modern paradigms to enable research development eigensolver algorithms. Furthermore, implementations some most recent methods. The purpose our article describe design framework. A performance comparison popular FORTRAN 77 code ARPACK given.
We describe an approach to nonlocal, nonlinear advection in one dimension that extends the usual pointwise concepts account for nonlocal contributions flux. The spatially operators we consider do not involve derivatives. Instead, spatial operator involves integral that, a distributional sense, reduces conventional advective operator. In particular, examine inviscid Burgers equation, which gives basic form with characterize properties associated well-posedness, and numerical results specific...
Abstract A nonlocal convection-diffusion model is introduced for the master equation of Markov jump processes in bounded domains. With minimal assumptions on parameters, steady and unsteady state equations are shown to be well-posed a weak sense. Then operator generator finite-range nonsymmetric and, when certain conditions parameters hold, generators finite infinite activity Lévy Lévy-type special instances operator.
The goal of our paper is to compare a number algorithms for computing large eigenvectors the generalized symmetric eigenvalue problem arising from modal analysis elastic structures. shift-invert Lanczos algorithm has emerged as workhorse solution this problem; however, sparse direct factorization required resulting set linear equations. Instead, considers use preconditioned iterative methods. We present brief review available eigensolvers followed by numerical comparison on three problems...
A mathematical framework for the coupling of atomistic and continuum models by blending them over a subdomain subject to constraint is developed. Using framework, four classes atomistic-to-continuum (AtC) methods are established, their consistency studied, relative merits discussed. In addition, helps clarify origin ghost forces formalizes notion patch test. Numerical experiments with AtC used illustrate theoretical results.
We introduce the Cauchy and time-dependent volume-constrained problems associated with a linear nonlocal convection-diffusion equation. These are shown to be well-posed correspond conventional equations as region of nonlocality vanishes. The also share number features such maximum principle, conservation dispersion relations, all which consistent their corresponding local counterparts. Moreover, these master for class finite activity Lévy-type processes nonsymmetric Lévy measure. Monte Carlo...