Remapping Algorithms Research Articles

Truly conserving with conservative remapping methods

Abstract. Conservative mapping of data from one horizontal grid to another should preserve certain integral or mean properties of the original data. This may be essential in some model applications, including ensuring realistic exchange of energy and mass between coupled model components. It can also be essential for certain types of analysis, such as evaluating how far a system is from an equilibrium state. For some common grids, existing remapping algorithms may fail to perfectly represent the shapes and sizes of grid cells, which leads to errors in the remapped fields. A procedure is presented here that enables users to rely on the mapping weights generated by remapping algorithms but corrects for their deficiencies. With this procedure, for a given pair of source and destination grids, a single set of remapping weights can be applied to remap any variable, including those with grid cells that are partially or fully masked.

Metrics for Intercomparison of Remapping Algorithms (MIRA) protocol applied to Earth system models

Abstract. Strongly coupled nonlinear phenomena such as those described by Earth system models (ESMs) are composed of multiple component models with independent mesh topologies and scalable numerical solvers. A common operation in ESMs is to remap or interpolate component solution fields defined on their computational mesh to another mesh with a different combinatorial structure and decomposition, e.g., from the atmosphere to the ocean, during the temporal integration of the coupled system. Several remapping schemes are currently in use or available for ESMs. However, a unified approach to compare the properties of these different schemes has not been attempted previously. We present a rigorous methodology for the evaluation and intercomparison of remapping methods through an independently implemented suite of metrics that measure the ability of a method to adhere to constraints such as grid independence, monotonicity, global conservation, and local extrema or feature preservation. A comprehensive set of numerical evaluations is conducted based on a progression of scalar fields from idealized and smooth to more general climate data with strong discontinuities and strict bounds. We examine four remapping algorithms with distinct design approaches, namely ESMF Regrid (Hill et al., 2004), TempestRemap (Ullrich and Taylor, 2015), generalized moving least squares (GMLS) (Trask and Kuberry, 2020) with post-processing filters, and WLS-ENOR (Li et al., 2020). By repeated iterative application of the high-order remapping methods to the test fields, we verify the accuracy of each scheme in terms of their observed convergence order for smooth data and determine the bounded error propagation using challenging, realistic field data on both uniform and regionally refined mesh cases. In addition to retaining high-order accuracy under idealized conditions, the methods also demonstrate robust remapping performance when dealing with non-smooth data. There is a failure to maintain monotonicity in the traditional L2-minimization approaches used in ESMF and TempestRemap, in contrast to stable recovery through nonlinear filters used in both meshless GMLS and hybrid mesh-based WLS-ENOR schemes. Local feature preservation analysis indicates that high-order methods perform better than low-order dissipative schemes for all test cases. The behavior of these remappers remains consistent when applied on regionally refined meshes, indicating mesh-invariant implementations. The MIRA intercomparison protocol proposed in this paper and the detailed comparison of the four algorithms demonstrate that the new schemes, namely GMLS and WLS-ENOR, are competitive compared to standard conservative minimization methods requiring computation of mesh intersections. The work presented in this paper provides a foundation that can be extended to include complex field definitions, realistic mesh topologies, and spectral element discretizations, thereby allowing for a more complete analysis of production-ready remapping packages.

Assessing the Accuracy of Different Remapping Methods in Adaptive Mesh Refinement

Additive manufacturing of metals has attracted much attention over the last years, promoting the development of several computational models for numerical simulation of the laser powder bed fusion (LPBF) process. Nevertheless, the finite element analysis of the LPBF process requires a large computational time. Thus, adaptive mesh refinement strategies are commonly adopted to reduce computational cost, which require some remapping procedure to transfer the state variables from the old mesh to the new one. The present study analyses two different remapping algorithms, namely the Inverse Isoparametric Mapping (IIM) and the Dual Kriging (DK) method. The IIM method uses the shape functions of the finite elements, while the DK method provides an explicit parametric interpolation. The case study adopted covers both coarsening and refinement procedures, using a mathematical function to define the mapped state variable. The accuracy of the remapping methods was lower in the refinement in comparison with the coarsening procedure. The error in the approximation is lower using the DK method in comparison with the IIM method. However, the IIM method does not suffer from error propagation in successive stages of either refinement/derefinement or coarsening/decoarsening.

MPR 1.0: a stand-alone multiscale parameter regionalization tool for improved parameter estimation of land surface models

Abstract. Distributed environmental models such as land surface models (LSMs) require model parameters in each spatial modeling unit (e.g., grid cell), thereby leading to a high-dimensional parameter space. One approach to decrease the dimensionality of the parameter space in these models is to use regularization techniques. One such highly efficient technique is the multiscale parameter regionalization (MPR) framework that translates high-resolution predictor variables (e.g., soil textural properties) into model parameters (e.g., porosity) via transfer functions (TFs) and upscaling operators that are suitable for every modeled process. This framework yields seamless model parameters at multiple scales and locations in an effective manner. However, integration of MPR into existing modeling workflows has been hindered thus far by hard-coded configurations and non-modular software designs. For these reasons, we redesigned MPR as a model-agnostic, stand-alone tool. It is a useful software for creating graphs of NetCDF variables, wherein each node is a variable and the links consist of TFs and/or upscaling operators. In this study, we present and verify our tool against a previous version, which was implemented in the mesoscale hydrologic model (mHM; https://www.ufz.de/mhm, last access: 16 January 2022). By using this tool for the generation of continental-scale soil hydraulic parameters applicable to different models (Noah-MP and HTESSEL), we showcase its general functionality and flexibility. Further, using model parameters estimated by the MPR tool leads to significant changes in long-term estimates of evapotranspiration, as compared to their default parameterizations. For example, a change of up to 25 % in long-term evapotranspiration flux is observed in Noah-MP and HTESSEL in the Mississippi River basin. We postulate that use of the stand-alone MPR tool will considerably increase the transparency and reproducibility of the parameter estimation process in distributed (environmental) models. It will also allow a rigorous uncertainty estimation related to the errors of the predictors (e.g., soil texture fields), transfer function and its parameters, and remapping (or upscaling) algorithms.

Mobility improvement of patients with peripheral visual field losses using novel see-through digital spectacles

PurposeTo evaluate see-through Augmented Reality Digital spectacles (AR DSpecs) for improving the mobility of patients with peripheral visual field (VF) losses when tested on a walking track.DesignProspective Case Series.Participants21 patients with peripheral VF defects in both eyes, with the physical ability to walk without assistance.MethodsWe developed the AR DSpecs as a wearable VF aid with an augmented reality platform. Image remapping algorithms produced personalized visual augmentation in real time based on the measured binocular VF with the AR DSpecs calibration mode. We tested the device on a walking track to determine if patients could more accurately identify peripheral objects.Main outcome measuresWe analyzed walking track scores (number of recognized/avoided objects) and eye tracking data (six gaze parameters) to measure changes in the kinematic and eye scanning behaviors while walking, and assessed a possible placebo effect by deactivating the AR DSpecs remapping algorithms in random trials.ResultsPerformance, judged by the object detection scores, improved with the AR DSpecs (P<0.001, Wilcoxon rank sum test) with an average improvement rate of 18.81%. Two gaze parameters improved with the activated algorithm (P<0.01, paired t-test), indicating a more directed gaze on the central path with less eye scanning. Determination of the binocular integrated VF with the DSpecs correlated with the integrated standard automated perimetry (R = 0.86, P<0.001), mean sensitivity difference 0.8 ± 2.25 dB (Bland-Altman).ConclusionsAR DSpecs may improve walking maneuverability of patients with peripheral VF defects by enhancing detection of objects in a testing environment.

Improving climate model coupling through a complete mesh representation: a case study with E3SM (v1) and MOAB (v5.x)

Abstract. One of the fundamental factors contributing to the spatiotemporal inaccuracy in climate modeling is the mapping of solution field data between different discretizations and numerical grids used in the coupled component models. The typical climate computational workflow involves evaluation and serialization of the remapping weights during the preprocessing step, which is then consumed by the coupled driver infrastructure during simulation to compute field projections. Tools like Earth System Modeling Framework (ESMF) (Hill et al., 2004) and TempestRemap (Ullrich et al., 2013) offer capability to generate conservative remapping weights, while the Model Coupling Toolkit (MCT) (Larson et al., 2001) that is utilized in many production climate models exposes functionality to make use of the operators to solve the coupled problem. However, such multistep processes present several hurdles in terms of the scientific workflow and impede research productivity. In order to overcome these limitations, we present a fully integrated infrastructure based on the Mesh Oriented datABase (MOAB) (Tautges et al., 2004; Mahadevan et al., 2015) library, which allows for a complete description of the numerical grids and solution data used in each submodel. Through a scalable advancing-front intersection algorithm, the supermesh of the source and target grids are computed, which is then used to assemble the high-order, conservative, and monotonicity-preserving remapping weights between discretization specifications. The Fortran-compatible interfaces in MOAB are utilized to directly link the submodels in the Energy Exascale Earth System Model (E3SM) to enable online remapping strategies in order to simplify the coupled workflow process. We demonstrate the superior computational efficiency of the remapping algorithms in comparison with other state-of-the-science tools and present strong scaling results on large-scale machines for computing remapping weights between the spectral element atmosphere and finite volume discretizations on the polygonal ocean grids.

Flexible telemanipulation based handy robot teaching on tape masking with complex geometry

Abstract Traditional robot teaching methods are cumbersome, tedious and difficult to scale for high-mix low-volume applications. The tape masking, a common process for surface protection before plasma spraying, spray painting and shot peening, is one of those domains where robotic automation lacks flexibility and reliability due to the complexity in task. Fortunately, it is still within the grasps of human-robot collaborative systems. This work presents a telemanipulation-based robot teaching framework that is able to let the robot manipulator cope with the taping tasks with complex workpiece geometries. The proposed framework allows quick calibration, variable motion mapping, and indexing so that the operators can easily set up and guide the robotic taping system to cover the tapes onto the layers and grooves of different workpieces. This framework enables the operators to change the motion mapping scale for both large-scale guidance and fine motion dexterous manipulation. Meanwhile, an indexing function makes it possible for the operators to re-map their poses from the edges of their comfortable regions. A portable VR system is applied in the telemanipulation system. With its six DoF motion precisely measured in real-time, the proposed motion remapping algorithms enable the operators to directly guide the robot in their selected scales. Experimental results show that the proposed framework facilitates robot programming on the manipulation of the complex workpieces that have multi-layer surfaces and grooves in between. It also reduces the teaching time comparing to other methods. This system and method improve teaching efficiency and convenience, which has potential value to be deployed in manufacturing.

Comparison of the Remapping Algorithms for the Advanced Technology Microwave Sounder (ATMS)

One of the limitations in using spaceborne, microwave radiometer data for atmospheric remote sensing is the nonuniform spatial resolution. Remapping algorithms can be applied to the data to ameliorate this limitation. In this paper, two remapping algorithms, the Backus–Gilbert inversion (BGI) technique and the filter algorithm (AFA), widely used in the operational data preprocessing of the Advanced Technology Microwave Sounder (ATMS), are investigated. The algorithms are compared using simulations and actual ATMS data. Results show that both algorithms can effectively enhance or degrade the resolution of the data. The BGI has a higher remapping accuracy than the AFA. It outperforms the AFA by producing less bias around coastlines and hurricane centers where the signal changes sharply. It shows no obvious bias around the scan ends where the AFA has a noticeable positive bias in the resolution-enhanced image. However, the BGI achieves the resolution enhancement at the expense of increasing the noise by 0.5 K. The use of the antenna pattern instead of the point spread function in the algorithm causes the persistent bias found in the AFA-remapped image, leading not only to an inaccurate antenna temperature expression but also to the neglect of the geometric deformation of the along-scan field-of-views.

On-GPU Thread-Data Remapping for Branch Divergence Reduction

General Purpose GPU computing (GPGPU) plays an increasingly vital role in high performance computing and other areas like deep learning. However, arising from the SIMD execution model, the branch divergence issue lowers efficiency of conditional branching on GPUs, and hinders the development of GPGPU. To achieve runtime on-the-spot branch divergence reduction, we propose the first on-GPU thread-data remapping scheme. Before kernel launching, our solution inserts codes into GPU kernels immediately before each target branch so as to acquire actual runtime divergence information. GPU software threads can be remapped to datasets multiple times during single kernel execution. We propose two thread-data remapping algorithms that are tailored to the GPU architecture. Effective on two generations of GPUs from both NVIDIA and AMD, our solution achieves speedups up to 2.718 with third-party benchmarks. We also implement three GPGPU frontier benchmarks from areas including computer vision, algorithmic trading and data analytics. They are hindered by more complex divergence coupled with different memory access patterns, and our solution works better than the traditional thread-data remapping scheme in all cases. As a compiler-assisted runtime solution, it can better reduce divergence for divergent applications that gain little acceleration on GPUs for the time being.

NCAR Release of CAM‐SE in CESM2.0: A Reformulation of the Spectral Element Dynamical Core in Dry‐Mass Vertical Coordinates With Comprehensive Treatment of Condensates and Energy

AbstractIt is the purpose of this paper to provide a comprehensive documentation of the new NCAR (National Center for Atmospheric Research) version of the spectral element (SE) dynamical core as part of the Community Earth System Model (CESM2.0) release. This version differs from previous releases of the SE dynamical core in several ways. Most notably the hybrid sigma vertical coordinate is based on dry air mass, the condensates are dynamically active in the thermodynamic and momentum equations (also referred to as condensate loading), and the continuous equations of motion conserve a more comprehensive total energy that includes condensates. Not related to the vertical coordinate change, the hyperviscosity operators and the vertical remapping algorithms have been modified. The code base has been significantly reduced, sped up, and cleaned up as part of integrating SE as a dynamical core in the CAM (Community Atmosphere Model) repository rather than importing the SE dynamical core from High‐Order Methods Modeling environment as an external code.

Fuzzy quality assessment of gridded approximations

Spatial data are often represented in a gridded format: a region of interest is overlayed with a raster, and every cell of the raster carries a value that is representative for the cell. Examples for this are e.g. air pollution concentrations or population densities provided on grids. A grid sometimes needs to be remapped onto a different grid, either for representation purposes or to allow operations or interactions with other gridded data, such as provided by the map algebra. Different approaches to remap gridded data exist and more recent approaches use other available data to improve the results. The emerging of these advanced remapping approaches also mandates the need for an objective method for ranking how different mappings conform to a known reference solution, as such a method allows to judge the performance of the different remapping algorithms. In this article, a fuzzy set based method to generate a family of ranking operators to objectively compare how different grids resemble a given reference grid is presented.

Assessment of remeshing and remapping strategies for large deformation elastoplastic Finite Element analysis

This work investigates the performance of various remeshing and remapping algorithms for the finite element simulation of plane-strain large deformation elastoplastic problems using a decoupled arbitrary Lagrangian–Eulerian approach. The remeshing algorithms, which are herein adjusted to the needs of elastoplastic deformation analyses, are the Elastic Rebound approach, the Spring Analogy Method and the Radial Basis Functions. The remapping algorithms are the Inverse Distance Algorithm and two data interpolation schemes, namely the Radial Basis Point Interpolation Functions and the Radial Basis Functions. The efficiency and robustness of the algorithms are assessed by simulating the penetration of a rigid flat punch.

1803 GPUやベクトル計算機における粒子リマッピングアルゴリズムの比較(OS18-1.計算力学におけるGPUコンピューティング(1),OS・一般セッション講演)

1803 GPUやベクトル計算機における粒子リマッピングアルゴリズムの比較(OS18-1.計算力学におけるGPUコンピューティング(1),OS・一般セッション講演)

HFTL: hybrid flash translation layer based on hot data identification for flash memory

For the last years, a number of flash translation layers (FTL) have been proposed for hiding erase-before-write architecture of NAND flash memory. However, although many conventional FTLs efficiently provide the logical to physical address remapping algorithms, they could not escape from the performance degradation when handling the hot data which tends to generate so many overwrites on the same logical address. In this paper, we propose a novel FTL algorithm called Hybrid Flash Translation Layer (HFTL) that adaptively exploits the sector mapping and log block based mapping schemes. To do so, HFTL first separates the hot data from the cold data by using the hot data identifier. And then it dynamically manages the former by using the sector mapping scheme showing an optimal performance for intensive overwrites at the same location, and the latter by using the log block based mapping scheme. By using this adaptive hybrid method, HFTL is always guaranteed to yield good performance for the pattern with the hot data as well as the pattern without it. Through a series of experiments, we show that HFTL yields better performance than conventional FTLs.

Reduced-dissipation remapping of velocity in staggered arbitrary Lagrangian–Eulerian methods

Remapping is an essential part of most Arbitrary Lagrangian–Eulerian (ALE) methods. In this paper, we focus on the part of the remapping algorithm that performs the interpolation of the fluid velocity field from the Lagrangian to the rezoned computational mesh in the context of a staggered discretization. Standard remapping algorithms generate a discrepancy between the remapped kinetic energy, and the kinetic energy that is obtained from the remapped nodal velocities which conserves momentum. In most ALE codes, this discrepancy is redistributed to the internal energy of adjacent computational cells which allows for the conservation of total energy. This approach can introduce oscillations in the internal energy field, which may not be acceptable. We analyze the approach introduced in Bailey (1984) [11] which is not supposed to introduce dissipation. On a simple example, we demonstrate a situation in which this approach fails. A modification of this approach is described, which eliminates (when it is possible) or reduces the energy discrepancy.

Adaptive decomposition and remapping algorithms for object-space-parallel direct volume rendering of unstructured grids

Object space (OS) parallelization of an efficient direct volume rendering algorithm for unstructured grids on distributed-memory architectures is investigated. The adaptive OS decomposition problem is modeled as a graph partitioning (GP) problem using an efficient and highly accurate estimation scheme for view-dependent node and edge weighting. In the proposed model, minimizing the cutsize corresponds to minimizing the parallelization overhead due to the data communication and redundant computation/storage while maintaining the GP balance constraint corresponds to maintaining the computational load balance in parallel rendering. A GP-based, view-independent cell clustering scheme is introduced to induce more tractable view-dependent computational graphs for successive visualizations. As another contribution, a graph-theoretical remapping model is proposed as a solution to the general remapping problem and is used in minimization of the cell-data migration overhead. The remapping tool RM-MeTiS is developed by modifying the GP tool MeTiS and is used in partitioning the remapping graphs. Experiments are conducted using benchmark datasets on a 28-node PC cluster to evaluate the performance of the proposed models.

NURBS-based surface grid redistribution and remapping algorithms

Algorithms to redistribute, refine, remap, and optimize structured surface grids utilized in computational fluid dynamics (CFD) simulations involving complex regimes are presented. The non-uniform rational B-spline (NURBS) representation is utilized for defining parametric surfaces. A semi-automatic remapping algorithm presented here results in a simplified surface grid generation process with significant reduction in generation labor time for surfaces involving holes, gaps and interior objects. A hermite transfinite interpolation method and elliptic generation systems are enhanced to optimize (in view of orthogonality and smoothness) surface grids. Computational examples are presented to demonstrate the success of these methodologies.