8 research outputs found
Canonical and Noncanonical Hamiltonian Operator Inference
A method for the nonintrusive and structure-preserving model reduction of
canonical and noncanonical Hamiltonian systems is presented. Based on the idea
of operator inference, this technique is provably convergent and reduces to a
straightforward linear solve given snapshot data and gray-box knowledge of the
system Hamiltonian. Examples involving several hyperbolic partial differential
equations show that the proposed method yields reduced models which, in
addition to being accurate and stable with respect to the addition of basis
modes, preserve conserved quantities well outside the range of their training
data
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
Albany: Using Component-based Design to Develop a Flexible, Generic Multiphysics Analysis Code
Abstract:
Albany is a multiphysics code constructed by assembling a set of reusable, general components. It is an implicit, unstructured grid finite element code that hosts a set of advanced features that are readily combined within a single analysis run. Albany uses template-based generic programming methods to provide extensibility and flexibility; it employs a generic residual evaluation interface to support the easy addition and modification of physics. This interface is coupled to powerful automatic differentiation utilities that are used to implement efficient nonlinear solvers and preconditioners, and also to enable sensitivity analysis and embedded uncertainty quantification capabilities as part of the forward solve. The flexible application programming interfaces in Albany couple to two different adaptive mesh libraries; it internally employs generic integration machinery that supports tetrahedral, hexahedral, and hybrid meshes of user specified order. We present the overall design of Albany, and focus on the specifics of the integration of many of its advanced features. As Albany and the components that form it are openly available on the internet, it is our goal that the reader might find some of the design concepts useful in their own work. Albany results in a code that enables the rapid development of parallel, numerically efficient multiphysics software tools. In discussing the features and details of the integration of many of the components involved, we show the reader the wide variety of solution components that are available and what is possible when they are combined within a simulation capability.
Key Words: partial differential equations, finite element analysis, template-based generic programmin
Trilinos/Kokkos-based strategy towards achieving a performance portable land-ice model
Non UBCUnreviewedAuthor affiliation: Sandia National LaboratoriesOthe
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
Optimal Compressed Sensing and Reconstruction of Unstructured Mesh Datasets
Abstract Exascale computing promises quantities of data too large to efficiently store and transfer across networks in order to be able to analyze and visualize the results. We investigate compressed sensing (CS) as an in situ method to reduce the size of the data as it is being generated during a large-scale simulation. CS works by sampling the data on the computational cluster within an alternative function space such as wavelet bases and then reconstructing back to the original space on visualization platforms. While much work has gone into exploring CS on structured datasets, such as image data, we investigate its usefulness for point clouds such as unstructured mesh datasets often found in finite element simulations. We sample using a technique that exhibits low coherence with tree wavelets found to be suitable for point clouds. We reconstruct using the stagewise orthogonal matching pursuit algorithm that we improved to facilitate automated use in batch jobs. We analyze the achievable compression ratios and the quality and accuracy of reconstructed results at each compression ratio. In the considered case studies, we are able to achieve compression ratios up to two orders of magnitude with reasonable reconstruction accuracy and minimal visual deterioration in the data. Our results suggest that, compared to other compression techniques, CS is attractive in cases where the compression overhead has to be minimized and where the reconstruction cost is not a significant concern
An Ice Sheet Model Validation Framework for the Greenland Ice Sheet
We propose a new ice sheet model validation framework – the Cryospheric Model Comparison Tool (CmCt) – that takes advantage of ice sheet altimetry and gravimetry observations collected over the past several decades and is applied here to modeling of the Greenland ice sheet. We use realistic simulations performed with the Community Ice Sheet Model (CISM) along with two idealized, non-dynamic models to demonstrate the framework and its use. Dynamic simulations with CISM are forced from 1991 to 2013, using combinations of reanalysis-based surface mass balance and observations of outlet glacier flux change. We propose and demonstrate qualitative and quantitative metrics for use in evaluating the different model simulations against the observations. We find that the altimetry observations used here are largely ambiguous in terms of their ability to distinguish one simulation from another. Based on basin-scale and whole-ice-sheet-scale metrics, we find that simulations using both idealized conceptual models and dynamic, numerical models provide an equally reasonable representation of the ice sheet surface (mean elevation differences of  \u3c  1 m). This is likely due to their short period of record, biases inherent to digital elevation models used for model initial conditions, and biases resulting from firn dynamics, which are not explicitly accounted for in the models or observations. On the other hand, we find that the gravimetry observations used here are able to unambiguously distinguish between simulations of varying complexity, and along with the CmCt, can provide a quantitative score for assessing a particular model and/or simulation. The new framework demonstrates that our proposed metrics can distinguish relatively better from relatively worse simulations and that dynamic ice sheet models, when appropriately initialized and forced with the right boundary conditions, demonstrate a predictive skill with respect to observed dynamic changes that have occurred on Greenland over the past few decades. An extensible design will allow for continued use of the CmCt as future altimetry, gravimetry, and other remotely sensed data become available for use in ice sheet model validation