Article

We propose a domain-decomposed method for Multivariate Functional Approximations (MFA) using B-spline bases, enhancing scalability and accuracy in large datasets. Our approach minimizes local errors and recovers high-order continuity at subdomain interfaces, optimizing communication costs. Performance results demonstrate its efficiency and scalability across various datasets in 1D, 2D, and 3D.

Compactly expressing large-scale datasets through Multivariate Functional Approximations (MFA) can be critically important for analysis and visualization to drive scientific discovery. Tackling such problems requires scalable data partitioning approaches to compute MFA representations in amenable wall clock times. We introduce a fully parallel scheme to reduce the total work per task in combination with an overlapping additive Schwarz-based iterative scheme to compute MFA with a tensor expansion of B-spline bases, while preserving full degree continuity across subdomain boundaries.

Fitting B-splines to discrete data is especially challenging when the given data contain noise, jumps, or corners. Here, we describe how periodic data sets with these features can be efficiently and robustly approximated with B-splines by analyzing the Fourier spectrum of the data. Our method uses a collection of spectral filters to produce different indicator functions that guide effective knot placement. In particular, we describe how spectral filters can be used to compute high-order derivatives, smoothed versions of noisy data, and the locations of jump discontinuities.

Coupled Earth System Models require transfer of field data between multiple components with varying spatial resolutions to determine the correct climate behavior. We present the Metrics for Intercomparison of Remapping Algorithms (MIRA) protocol to evaluate the accuracy, conservation properties, monotonicity and local feature preservation of four different remapper algorithms, for various unstructured mesh problems of interest. Future extensions to more practical use cases are also discussed.

Accurate climate modeling of coupled Earth systems requires mapping of solution field data between dependent components that use non-matching discrete meshes. While existing workflows provide a pathway to generate the projection weights as an offline step, severe bottlenecks impede flexible setup of high-resolution models. In this paper, we present new algorithmic approaches to simplify the E3SM computational workflow using a scalable software infrastructure to generate the remapping operators.

We investigate the representation of discrete scientific data with a $C^k$ functional model, where $C^k$ denotes $k$-th order …

A multi-degree, multi-dimensional and multi-level array-based hierarchical mesh refinement capability through uniform refinement of unstructured meshes for efficient solution of PDE’s using finite element methods and multigrid solvers is presented. The framework is designed to generate nested hierarchies from an initial coarse mesh that can be used for a variety of purposes such as in multigrid solvers/preconditioners, to do solution convergence and verification studies and to improve overall parallel efficiency by decreasing I/O bandwidth requirements.

Implicit Runge Kutta (IRK) methods were applied to solve the nonlinear point reactor kinetic equations with feedback. These methods …