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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.

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.

An integrated multi-physics simulation capability for the design and analysis of current and future nuclear reactor models is being investigated, to tightly couple neutron transport and thermal-hydraulics physics under the SHARP framework. Over several years, high-fidelity, validated mono-physics solvers with proven scalability on petascale architectures have been developed independently. Based on a unified component-based architecture, these existing codes can be coupled with a mesh-data backplane and a flexible coupling-strategy-based driver suite to produce a viable tool for analysts.

The modeling of nuclear reactors involves the solution of a multiphysics problem with various time and length scales. This paper deals with the verification aspects associated with a multiphysics code, i.e., the substantiation that the mathematical description of the multiphysics equations are solved correctly (in time and space).

A domain decomposed Monte Carlo communication kernel is used to carry out performance tests to establish the feasibility of using Monte Carlo techniques for practical Light Water Reactor (LWR) core analyses. The results of the prototype code are interpreted in the context of simplified performance models which elucidate key scaling regimes of the parallel algorithm.

Conventional coupling paradigms currently used to couple different physics components in reactor analysis problems can be inconsistent in their treatment of the nonlinear terms due to the operator-split (OS) strategies employed. This leads to the usage of small time steps to maintain accuracy requirements, thereby increasing the overall computational time. This paper proposes some remedies to OS techniques that can restore consistency in the coupling of the nonlinear terms and explores high-order mono-block nonlinearly consistent techniques with time step control.