No abstract

Summary Reduced order models are useful for accelerating simulations in many‐query contexts, such as optimization, uncertainty quantification, and sensitivity analysis. However, offline training of reduced order models (ROMs) can have prohibitively expensive memory and floating‐point operation costs in high‐performance computing applications, where memory per core is limited. To overcome this limitation for proper orthogonal decomposition, we propose a novel adaptive selection method for snapshots in time that limits offline training costs by selecting snapshots according an error control mechanism similar to that found in adaptive time‐stepping ordinary differential equation solvers. The error estimator used in this work is related to theory bounding the approximation error in time of proper orthogonal decomposition‐based ROMs, and memory usage is minimized by computing the singular value decomposition using a single‐pass incremental algorithm. Results for a viscous Burgers' test problem demonstrate convergence in the limit as the algorithm error tolerances go to zero; in this limit, the full‐order model is recovered to within discretization error. A parallel version of the resulting method can be used on supercomputers to generate proper orthogonal decomposition‐based ROMs, or as a subroutine within hyperreduction algorithms that require taking snapshots in time, or within greedy algorithms for sampling parameter space. Copyright © 2016 John Wiley & Sons, Ltd.

Mesh-based PDE simulation codes are becoming increasingly sophisticated and rely on advanced meshing and discretization tools. Unfortunately, it is still difficult to interchange or interoperate tools developed by different communities to experiment with various technologies or to develop new capabilities. To address these difficulties, we have developed component interfaces designed to support the information flow of mesh-based PDE simulations. We describe this information flow and discuss typical roles and services provided by the geometry, mesh, and field components of the simulation. Based on this delineation for the roles of each component, we give a high-level description of the abstract data model and set of interfaces developed by the Department of Energy's Interoperable Tools for Advanced Petascale Simulation (ITAPS) center. These common interfaces are critical to our interoperability goal, and we give examples of several services based upon these interfaces including mesh adaptation and mesh improvement.

‡ Brand presents multiple algorithms in his original conference paper on the incremental SVD. Here, we present the "naïve" version of Brand's incremental SVD algorithm using single-column updates, for simplicity. § Specifically, Brand recommends modified Gram-Schmidt orthogonalization [9]; thin QR works well in practice. || In the derivation, both linearity of the diag. / operator and the identity diag.Ax/y D diag.y/Ax are used; this identity holds for all matrices A and all vectors x and y that can be premultiplied by A.

SUMMARYThis paper presents a method for generating computational meshes by building structured component grids and then connecting them with an unstructured mesh. The approach uses technologies from the overset grid community, specifically the Ogen overlapping grid generator from the Overture framework, to build a collection of overlapping structured grids for a given geometry. Overlapping regions between the component grids are automatically removed and replaced with an unstructured mesh that conforms to the boundaries of the holes in the structured grids. Large regions of high-quality structured grids comprise most of the domain and are connected by a comparatively small amount of unstructured mesh. A method for generating hybrid surface meshes from overlapping and intersecting surface grids is also described. These surface meshes preserve the geometry used to generate the structured grids by querying the original geometry database. An implementation of advancing front mesh generation creates the interstitial surface and volume unstructured meshes. Mesh spacing information is automatically computed from the original overlapping grid. The mesh is optimized by regeneration in areas of poor quality as well as vertex repositioning by non-linear optimization of a quality metric. Quality assessment is accomplished by incorporating the mesh spacing information into algebraic mesh quality metrics. A description of the approach and algorithms is presented followed by two-and three-dimensional demonstrations. Published in 2004 by John Wiley & Sons, Ltd.