Paul Kuberry

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

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...

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...

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...

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,...

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...

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)...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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,...

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....

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...

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...

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...

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...