arXiv subjects

Paul Kuberry

Publications and source records attributed to Paul Kuberry.

6 recordsLinked to original sources

arXiv2025

Trilinos: Enabling Scientific Computing Across Diverse Hardware Architectures at Scale

Trilinos is a community-developed, open-source software framework that facilitates building large-scale, complex, multiscale, multiphysics simulation code bases for scientific and engineering problems. Since the Trilinos framework has undergone substantial changes to support new applications and new hardware architectures, this document is an update to ``An Overview of the Trilinos project'' by Heroux et al. (ACM Transactions on Mathematical Software, 31(3):397-423, 2005). It describes the design of Trilinos, introduces its new organization in product areas, and highlights established and new features available in Trilinos. Particular focus is put on the modernized software stack based on the Kokkos ecosystem to deliver performance portability across heterogeneous hardware architectures. This paper also outlines the organization of the Trilinos community and the contribution model to help onboard interested users and contributors.

cs.MS↗

arXiv2024

An optimization-based coupling of reduced order models with efficient reduced adjoint basis generation approach

Optimization-based coupling (OBC) is an attractive alternative to traditional Lagrange multiplier approaches in multiple modeling and simulation contexts. However, application of OBC to time-dependent problems has been hindered by the computational cost of finding the stationary points of the associated Lagrangian, which requires primal and adjoint solves. This issue can be mitigated by using OBC in conjunction with computationally efficient reduced order models (ROM). To demonstrate the potential of this combination, in this paper we develop an optimization-based ROM-ROM coupling for a transient advection-diffusion transmission problem. We pursue the ``optimize-then-reduce'' path towards solving the minimization problem at each timestep and solve reduced-space adjoint system of equations, where the main challenge in this formulation is the generation of adjoint snapshots and reduced bases for the adjoint systems required by the optimizer. One of the main contributions of the paper is a new technique for efficient adjoint snapshot collection for gradient-based optimizers in the context of optimization-based ROM-ROM couplings. We present numerical studies demonstrating the accuracy of the approach along with comparison between various approaches for selecting a reduced order basis for the adjoint systems, including decay of snapshot energy, average iteration counts, and timings.

cs.CE↗

arXiv2024

Non-intrusive data-driven model order reduction for circuits based on Hammerstein architectures

We demonstrate that system identification techniques can provide a basis for effective, non-intrusive model order reduction (MOR) for common circuits that are key building blocks in microelectronics. Our approach is motivated by the practical operation of these circuits and utilizes a canonical Hammerstein architecture. To demonstrate the approach we develop parsimonious Hammerstein models for a nonlinear CMOS differential amplifier and an operational amplifier circuit. We train these models on a combination of direct current (DC) and transient Spice circuit simulation data using a novel sequential strategy to identify their static nonlinear and linear dynamical parts. Simulation results show that the Hammerstein model is an effective surrogate for for these types of circuits that accurately and efficiently reproduces their behavior over a wide range of operating points and input frequencies.

eess.SY↗

arXiv2024

Dynamic flux surrogate-based partitioned methods for interface problems

Loosely coupled partitioned methods for multiphysics problems treat each subproblem as a separate entity and advance them independently in time. In so doing these methods enable code reuse, increase concurrency and provide a convenient framework for plug-and-play multiphysics simulations. However, mathematically loosely coupled schemes are equivalent to a single step of an iterative solution method, which can compromise their accuracy and stability. We present a new data-driven partitioned method for coupled parametric PDEs that can improve upon the accuracy of traditional loosely coupled methods without incurring a performance penalty. To that end, we replace conventional field transfers across the interface by a surrogate for the dynamics of the interface flux exchanged between the subdomains. To develop this surrogate we apply dynamic mode decomposition to a non-standard staggered-in-time state, comprising the interface flux and small solution patches near the interface. The new approach shifts the main computational burden to an offline training phase, whereas application of the surrogate in the online phase amounts to a single matrix-vector multiplication. We provide stability analysis of the surrogate-based partitioned scheme and include numerical results that demonstrate its potential.

cs.CE↗

arXiv2023

Explicit synchronous partitioned scheme for coupled reduced order models based on composite reduced bases

This paper formulates, analyzes, and demonstrates numerically a method for the partitioned solution of coupled interface problems involving combinations of projection-based reduced order models (ROM) and/or full order methods (FOMs). The method builds on the partitioned scheme developed in [1], which starts from a well-posed formulation of the coupled interface problem and uses its dual Schur complement to obtain an approximation of the interface flux. Explicit time integration of this problem decouples its subdomain equations and enables their independent solution on each subdomain. Extension of this partitioned scheme to coupled ROM-ROM or ROM-FOM problems required formulations with non-singular Schur complements. To obtain these problems, we project a well-posed coupled FOM-FOM problem onto a composite reduced basis comprising separate sets of basis vectors for the interface and interior variables, and use the interface reduced basis as a Lagrange multiplier. Our analysis confirms that the resulting coupled ROM-ROM and ROM-FOM problems have provably non-singular Schur complements, independent of the mesh size and the reduced basis size. In the ROM-FOM case, analysis shows that one can also use the interface FOM space as a Lagrange multiplier. We illustrate the theoretical and computational properties of the partitioned scheme through reproductive and predictive tests for a model advection-diffusion transmission problem.

math.NA↗

arXiv2022

A Novel Partitioned Approach for Reduced Order Model -- Finite Element Model (ROM-FEM) and ROM-ROM Coupling

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 projection-based reduced order models (ROMs), introduced to lower the computational cost associated with a particular component. We simulate this scenario by considering a model interface problem that is discretized independently on two non-overlapping subdomains. We then formulate a partitioned scheme for this problem that allows the coupling between a ROM "code" for one of the subdomains with a finite element model (FEM) or ROM "code" for the other subdomain. The ROM "codes" are constructed by performing proper orthogonal decomposition (POD) on a snapshot ensemble to obtain a low-dimensional reduced order basis, followed by a Galerkin projection onto this basis. The ROM and/or FEM "codes" on each subdomain are then coupled using a Lagrange multiplier representing the interface flux. To partition the resulting monolithic problem, we first eliminate the flux through a dual Schur complement. Application of an explicit time integration scheme to the transformed monolithic problem decouples the subdomain equations, allowing their independent solution for the next time step. We show numerical results that demonstrate the proposed method's efficacy in achieving both ROM-FEM and ROM-ROM coupling.

math.NA↗