Paul Kuberry

Paul Kuberry
Sandia National Laboratories · Division of Computation, Computers, Information and Mathematics

Ph.D., Mathematical Sciences, Clemson University

About

45
Publications
4,915
Reads
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172
Citations
Introduction
Paul Kuberry currently works at the Center for Computing Research at Sandia National Laboratories as an applied mathematician and software developer. His research interests include developing and analyzing algorithms and coupling methods for the solution of multi-physics partial differential equations and problems posed on domains with mismatched interfaces. https://cfwebprod.sandia.gov/cfdocs/CompResearch/templates/insert/profile.cfm?pakuber http://www.paulkuberry.com
Additional affiliations
April 2017 - present
Sandia National Laboratories
Position
  • Senior Member of Technical Staff
May 2015 - April 2017
Sandia National Laboratories
Position
  • PhD Student
May 2013 - August 2013
United States Naval Research Laboratory
Position
  • Naval Research Enterprise Intern
Description
  • Investigated model reduction techniques for nonlinear ordinary differential equations for use in reactive flow solvers.
Education
August 2010 - May 2015
Clemson University
Field of study
  • Mathematical Sciences

Publications

Publications (45)
Preprint
Partitioned methods allow one to build a simulation capability for coupled problems by reusing existing single-component codes. In so doing, partitioned methods can shorten code development and validation times for multiphysics and multiscale applications. In this work, we consider a scenario in which one or more of the "codes" being coupled are pr...
Article
We develop numerical methods for computing statistics of stochastic processes on surfaces of general shape with drift-diffusion dynamics dXt=a(Xt)dt+b(Xt)dWt. We formulate descriptions of Brownian motion and general drift-diffusion processes on surfaces. We consider statistics of the form u(x)=Ex[∫0τg(Xt)dt]+Ex[f(Xτ)] for a domain Ω and the exit st...
Code
The Compadre Toolkit provides a performance portable solution for the parallel evaluation of computationally dense kernels. The toolkit specifically targets the Generalized Moving Least Squares (GMLS) approach, which requires the inversion of small dense matrices. The result is a set of weights that provide the information needed for remap or entri...
Preprint
Full-text available
Strongly coupled nonlinear phenomena such as those described by Earth System Models (ESM) are composed of multiple component models with independent mesh topologies and scalable numerical solvers. A common operation in ESM is to remap or interpolate results from one component's computational mesh to another, e.g., from the atmosphere to the ocean,...
Preprint
Full-text available
A parallel implementation of a compatible discretization scheme for steady-state Stokes problems is presented in this work. The scheme uses generalized moving least squares to generate differential operators and apply boundary conditions. This meshless scheme allows a high-order convergence for both the velocity and pressure, while also incorporate...
Preprint
Full-text available
We develop numerical methods for computing statistics of stochastic processes on surfaces of general shape with drift-diffusion dynamics $d{X}_t = a({X}_t)dt + {b}({X}_t)d{W}_t$. We consider on a surface domain $\Omega$ the statistics $u(\mathbf{x}) = \mathbb{E}^{\mathbf{x}}\left[\int_0^\tau g(X_t)dt \right] + \mathbb{E}^{\mathbf{x}}\left[f(X_\tau)...
Code
The Compadre (Compatible Particle Discretization and Remap) Toolkit provides a performance portable solution for the parallel evaluation of computationally dense kernels. The toolkit specifically targets the Generalized Moving Least Squares (GMLS) approach, which requires the inversion of small dense matrices. The result is a set of weights that pr...
Technical Report
Full-text available
This report summarizes the work performed under a one-year LDRD project aiming to enable accurate and robust numerical simulation of partial differential equations for meshes that are of poor quality. Traditional finite element methods use the mesh to both discretize the geometric domain and to define the finite element shape functions. The latter...
Conference Paper
Compact semiconductor device models are essential for efficiently designing and analyzing large circuits. However, traditional compact model development requires a large amount of manual effort and can span many years. Moreover, inclusion of new physics (\eg{}, radiation effects) into an existing model is not trivial and may require redevelopment f...
Code
The Compadre (Compatible Particle Discretization and Remap) Toolkit provides a performance portable solution for the parallel evaluation of computationally dense kernels. The toolkit specifically targets the Generalized Moving Least Squares (GMLS) approach, which requires the inversion of small dense matrices. The result is a set of weights that pr...
Article
Full-text available
Component coupling is a crucial part of climate models, such as DOE’s E3SM (Caldwell et al., 2019). A common coupling strategy in climate models is for their components to exchange flux data from the previous time-step. This approach effectively performs a single step of an iterative solution method for the monolithic coupled system, which may lead...
Code
The Compadre (Compatible Particle Discretization and Remap) Toolkit provides a performance portable solution for the parallel evaluation of computationally dense kernels. The toolkit specifically targets the Generalized Moving Least Squares (GMLS) approach, which requires the inversion of small dense matrices. The result is a set of weights that pr...
Chapter
In most finite element methods the mesh is used to both represent the domain and to define the finite element basis. As a result the quality of such methods is tied to the quality of the mesh and may suffer when the latter deteriorates. This paper formulates an alternative approach, which separates the discretization of the domain, i.e., the meshin...
Article
Full-text available
We utilize generalized moving least squares (GMLS) to develop meshfree techniques for discretizing hydrodynamic flow problems on manifolds. We use exterior calculus to formulate incompressible hydrodynamic equations in the Stokesian regime and handle the divergence-free constraints via a generalized vector potential. This provides less coordinate-c...
Preprint
Full-text available
Compact semiconductor device models are essential for efficiently designing and analyzing large circuits. However, traditional compact model development requires a large amount of manual effort and can span many years. Moreover, inclusion of new physics (eg, radiation effects) into an existing compact model is not trivial and may require redevelopm...
Code
The Compadre (Compatible Particle Discretization and Remap) Toolkit provides a performance portable solution for the parallel evaluation of computationally dense kernels. The toolkit specifically targets the Generalized Moving Least Squares (GMLS) approach, which requires the inversion of small dense matrices. The result is a set of weights that pr...
Article
Full-text available
In the present study, we propose a novel multiphysics model that merges two time-dependent problems -- the Fluid-Structure Interaction (FSI) and the ultrasonic wave propagation in a fluid-structure domain with a one directional coupling from the FSI problem to the ultrasonic wave propagation problem. This model is referred to as the ``eXtended flui...
Article
Meshfree discretization of surface partial differential equations is appealing, due to their ability to naturally adapt to deforming motion of the underlying manifold. In this work, we consider an existing scheme proposed by Liang et al. reinterpreted in the context of generalized moving least squares (GMLS), showing that existing numerical analysi...
Preprint
Full-text available
We utilize generalized moving least squares (GMLS) to develop meshfree techniques for discretizing hydrodynamic flow problems on manifolds. We use exterior calculus to formulate incompressible hydrodynamic equations in the Stokesian regime and handle the divergence-free constraints via a generalized vector potential. This provides less coordinate-c...
Article
Full-text available
The present study introduces the coupled multiphysics model as part of the structural health monitoring (SHM) system. In particular, the Ultrasonic Guided Waves (UGWs) propagation is tracked in order to identify the damage to the structure. For this purpose, a multiphysics mathematical model is proposed. The model constitutes a monolithically coupl...
Preprint
Full-text available
In most finite element methods the mesh is used to both represent the domain and to define the finite element basis. As a result the quality of such methods is tied to the quality of the mesh and may suffer when the latter deteriorates. This paper formulates an alternative approach, which separates the discretization of the domain, i.e., the meshin...
Preprint
Full-text available
Meshfree discretization of surface partial differential equations are appealing, due to their ability to naturally adapt to deforming motion of the underlying manifold. In this work, we consider an existing scheme proposed by Liang et al. reinterpreted in the context of generalized moving least squares (GMLS), showing that existing numerical analys...
Code
The Compadre Toolkit provides a performance portable solution for the parallel evaluation of computationally dense kernels. The toolkit specifically targets the Generalized Moving Least Squares (GMLS) approach, which requires the inversion of small dense matrices. The result is a set of weights that provide the information needed for remap or entri...
Code
The Compadre (Compatible Particle Discretization and Remap) Toolkit provides a performance portable solution for the parallel evaluation of computationally dense kernels. The toolkit specifically targets the Generalized Moving Least Squares (GMLS) approach, which requires the inversion of small dense matrices. The result is a set of weights that pr...
Code
The Compadre Toolkit solves a minimization problem, that once solved allows a user to reconstruct a function from sample data collected from a cloud of data sites. The solution to this minimization can also be used to assemble a linear system that can be solved numerically using some other software. The minimization problem the toolkit solves is to...
Article
Traditional explicit partitioned schemes exchange boundary conditions between subdomains and can be related to iterative solution methods for the coupled problem. As a result, these schemes may require multiple subdomain solves, acceleration techniques, or optimized transmission conditions to achieve sufficient accuracy and/or stability. We present...
Conference Paper
Full-text available
We present an optimization approach with two controls for coupling elliptic partial differential equations posed on subdomains sharing an interface that is discretized independently on each subdomain, introducing gaps and overlaps. We use two virtual Neu-mann controls, one defined on each discrete interface, thereby eliminating the need for a virtu...
Article
Independent meshing of subdomains in interface problems can lead to spatially non- coincident interface grids. This setting occurs both when the interface is physical, as in transmission problems, and when it results from breaking up a complex domain into simpler shapes to aid grid generation, as in mesh tying. Traditional domain decomposition enfo...
Conference Paper
Full-text available
This contribution is the second part of three papers on Adaptive Multigrid Methods for the eXtended Fluid-Structure Interaction (eXFSI) Problem, where we introduce a monolithic variational formulation and solution techniques. To the best of our knowledge, such a model is new in the literature. This model is used to design an on-line structural heal...
Article
Full-text available
Building off of previous analytical results for recasting fluid-structure interaction into an optimal control setting, an a priori error estimate is given for the optimality system by means of BRR theory. The convergence of the steepest descent method is proven in a discrete setting for a sufficiently small time step and mesh size. A numerical stud...
Article
Fluid-structure interaction (FSI) simulation presents many computational difficulties, particularly when the densities of the fluid and structure are close. A previous report [P. Kuberry and H. Lee, Comput. Methods Appl. Mech. Engrg., 267 (2013), pp. 594--605] has suggested that recasting the FSI problem in the context of optimal control may signif...
Thesis
Fluid-structure interaction (FSI) is ubiquitous in both manufacturing and nature. At the same time, models describing this phenomenon are highly sensitive and nonlinear. Providing an analytical solution to these models for a realistic set of initial and boundary conditions has proven to be intractable. Within the domain of computational simulation,...
Conference Paper
Full-text available
We present a new explicit algorithm for linear elastodynamic problems with material interfaces. The method discretizes the governing equations independently on each material subdomain and then connects them by exchanging forces and masses across the material interface. Variational flux recovery techniques provide the force and mass approximations....
Technical Report
Full-text available
Fluid-structure interaction simulation presents many computational difficulties, particularly when the densities of the fluid and structure are close. A previous report [20] has suggested that recasting the FSI problem in the context of optimal control may significantly reduce computation time. This report introduces a Neumann type control along wi...
Article
Full-text available
Simulating fluid-structure interactions is challenging due to the tight coupling between the fluid and solid substructures. Explicit and implicit decoupling methods often either fail or require relaxation when densities of the two materials are close. In this paper, a fluid-structure interaction problem is formulated as a least squares problem, whe...
Article
Full-text available
Interface problems modeled by differential equations have many applications in mathematical biology, fluid mechanics, material sciences, and many other areas. Typically, interface problems are characterized by discontinuities in the coefficients and/or the Dirac delta function singularities in the source term. Because of these irregularities, solut...
Article
We study Voigt regularizations for the Navier–Stokes equations (NSEs) and magnetohydrodynamic (MHD) equations in the presence of physical boundary conditions. In particular, we develop the first finite element numerical algorithms for these systems, prove stability and convergence of the algorithms, and test them computationally on problems of prac...

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