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NASA NTRS1996

Global Load Balancing with Parallel Mesh Adaption on Distributed-Memory Systems

Dynamic mesh adaptation on unstructured grids is a powerful tool for efficiently computing unsteady problems to resolve solution features of interest. Unfortunately, this causes load inbalances among processors on a parallel machine. This paper described the parallel implementation of a tetrahedral mesh adaption scheme and a new global load balancing method. A heuristic remapping algorithm is presented that assigns partitions to processors such that the redistribution coast is minimized. Results indicate that the parallel performance of the mesh adaption code depends on the nature of the adaption region and show a 35.5X speedup on 64 processors of an SP2 when 35 percent of the mesh is randomly adapted. For large scale scientific computations, our load balancing strategy gives an almost sixfold reduction in solver execution times over non-balanced loads. Furthermore, our heuristic remappier yields processor assignments that are less than 3 percent of the optimal solutions, but requires only 1 percent of the computational time.

Biswas, Rupak↗

NASA NTRS2019

Fundamental Improvement of a Convergence Test for Iterative Strain-Gage Balance Load Predictions

A fundamental improvement of a convergence test for wind tunnel strain-gage balance load iterations was developed. The improvement became necessary because incorrect test results were obtained whenever the original test was applied to multi-component balances with large load capacity differences. The original test was first published in NASA TN D-6860. It uses an upper bound of the Lipschitz constant to assess convergence characteristics of balance load predictions whenever the Iterative Method is applied. The Lipschitz constant is a function of the partial derivatives of each balance load component with respect to all other load components. Unfortunately, the original definition of the convergence test overlooked the fact that the Lipschitz constant is a dimensionless quantity and that the partial derivative of one load component with respect to another load component is not always dimensionless. Therefore, an improvement of the original test was successfully developed that uses load capacities to make all inputs for the calculation of the Lipschitz constant dimensionless before use. Results from the calibration data analysis of a six-component force balance and a five-component semi-span balance are used to illustrate the application of the improved load iteration convergence test.

Strain-Gage Balance↗

NASA NTRS2012

Influence of Primary Gage Sensitivities on the Convergence of Balance Load Iterations

The connection between the convergence of wind tunnel balance load iterations and the existence of the primary gage sensitivities of a balance is discussed. First, basic elements of two load iteration equations that the iterative method uses in combination with results of a calibration data analysis for the prediction of balance loads are reviewed. Then, the connection between the primary gage sensitivities, the load format, the gage output format, and the convergence characteristics of the load iteration equation choices is investigated. A new criterion is also introduced that may be used to objectively determine if the primary gage sensitivity of a balance gage exists. Then, it is shown that both load iteration equations will converge as long as a suitable regression model is used for the analysis of the balance calibration data, the combined influence of non linear terms of the regression model is very small, and the primary gage sensitivities of all balance gages exist. The last requirement is fulfilled, e.g., if force balance calibration data is analyzed in force balance format. Finally, it is demonstrated that only one of the two load iteration equation choices, i.e., the iteration equation used by the primary load iteration method, converges if one or more primary gage sensitivities are missing. This situation may occur, e.g., if force balance calibration data is analyzed in direct read format using the original gage outputs. Data from the calibration of a six component force balance is used to illustrate the connection between the convergence of the load iteration equation choices and the existence of the primary gage sensitivities.

Ulbrich, Norbert Manfred↗

NASA NTRS1990

Method of up-front load balancing for local memory parallel processors

In a parallel processing computer system with multiple processing units and shared memory, a method is disclosed for uniformly balancing the aggregate computational load in, and utilizing minimal memory by, a network having identical computations to be executed at each connection therein. Read-only and read-write memory are subdivided into a plurality of process sets, which function like artificial processing units. Said plurality of process sets is iteratively merged and reduced to the number of processing units without exceeding the balance load. Said merger is based upon the value of a partition threshold, which is a measure of the memory utilization. The turnaround time and memory savings of the instant method are functions of the number of processing units available and the number of partitions into which the memory is subdivided. Typical results of the preferred embodiment yielded memory savings of from sixty to seventy five percent.

Baffes, Paul Thomas↗

NASA NTRS2010

Comparison of Iterative and Non-Iterative Strain-Gage Balance Load Calculation Methods

The accuracy of iterative and non-iterative strain-gage balance load calculation methods was compared using data from the calibration of a force balance. Two iterative and one non-iterative method were investigated. In addition, transformations were applied to balance loads in order to process the calibration data in both direct read and force balance format. NASA's regression model optimization tool BALFIT was used to generate optimized regression models of the calibration data for each of the three load calculation methods. This approach made sure that the selected regression models met strict statistical quality requirements. The comparison of the standard deviation of the load residuals showed that the first iterative method may be applied to data in both the direct read and force balance format. The second iterative method, on the other hand, implicitly assumes that the primary gage sensitivities of all balance gages exist. Therefore, the second iterative method only works if the given balance data is processed in force balance format. The calibration data set was also processed using the non-iterative method. Standard deviations of the load residuals for the three load calculation methods were compared. Overall, the standard deviations show very good agreement. The load prediction accuracies of the three methods appear to be compatible as long as regression models used to analyze the calibration data meet strict statistical quality requirements. Recent improvements of the regression model optimization tool BALFIT are also discussed in the paper.

Ulbrich, N.↗

NASA NTRS2016

Assessment of the Uniqueness of Wind Tunnel Strain-Gage Balance Load Predictions

A new test was developed to assess the uniqueness of wind tunnel strain-gage balance load predictions that are obtained from regression models of calibration data. The test helps balance users to gain confidence in load predictions of non-traditional balance designs. It also makes it possible to better evaluate load predictions of traditional balances that are not used as originally intended. The test works for both the Iterative and Non-Iterative Methods that are used in the aerospace testing community for the prediction of balance loads. It is based on the hypothesis that the total number of independently applied balance load components must always match the total number of independently measured bridge outputs or bridge output combinations. This hypothesis is supported by a control volume analysis of the inputs and outputs of a strain-gage balance. It is concluded from the control volume analysis that the loads and bridge outputs of a balance calibration data set must separately be tested for linear independence because it cannot always be guaranteed that a linearly independent load component set will result in linearly independent bridge output measurements. Simple linear math models for the loads and bridge outputs in combination with the variance inflation factor are used to test for linear independence. A highly unique and reversible mapping between the applied load component set and the measured bridge output set is guaranteed to exist if the maximum variance inflation factor of both sets is less than the literature recommended threshold of five. Data from the calibration of a six{component force balance is used to illustrate the application of the new test to real-world data.

strain-gage balance↗

NASA NTRS1996

Impact of Load Balancing on Unstructured Adaptive Grid Computations for Distributed-Memory Multiprocessors

The computational requirements for an adaptive solution of unsteady problems change as the simulation progresses. This causes workload imbalance among processors on a parallel machine which, in turn, requires significant data movement at runtime. We present a new dynamic load-balancing framework, called JOVE, that balances the workload across all processors with a global view. Whenever the computational mesh is adapted, JOVE is activated to eliminate the load imbalance. JOVE has been implemented on an IBM SP2 distributed-memory machine in MPI for portability. Experimental results for two model meshes demonstrate that mesh adaption with load balancing gives more than a sixfold improvement over one without load balancing. We also show that JOVE gives a 24-fold speedup on 64 processors compared to sequential execution.

Biswas, Rupak↗

NASA NTRS1996

Impact of Load Balancing on Unstructured Adaptive Grid Computations for Distributed-Memory Multiprocessors

Sohn, Andrew↗

NASA NTRS1995

Multithreaded Model for Dynamic Load Balancing Parallel Adaptive PDE Computations

We present a multithreaded model for the dynamic load-balancing of numerical, adaptive computations required for the solution of Partial Differential Equations (PDE's) on multiprocessors. Multithreading is used as a means of exploring concurrency in the processor level in order to tolerate synchronization costs inherent to traditional (non-threaded) parallel adaptive PDE solvers. Our preliminary analysis for parallel, adaptive PDE solvers indicates that multithreading can be used an a mechanism to mask overheads required for the dynamic balancing of processor workloads with computations required for the actual numerical solution of the PDE's. Also, multithreading can simplify the implementation of dynamic load-balancing algorithms, a task that is very difficult for traditional data parallel adaptive PDE computations. Unfortunately, multithreading does not always simplify program complexity, often makes code re-usability not an easy task, and increases software complexity.

Chrisochoides, Nikos↗

NASA NTRS2018

Implementation and Use of a Convergence Test for Iterative Wind Tunnel Balance Load Predictions

A modified and extended version of a convergence test for wind tunnel strain-gage balance load iterations was implemented. The test uses an upper bound of the Lipschitz constant to assess convergence characteristics of balance load predictions if the Iterative Method is applied. Convergence is expected within the use envelope of the balance whenever this upper bound is less than the threshold of one. It is explained in great detail how the convergence test can be applied to the two load iteration equation types that are currently being used in the aerospace testing community. In addition, the application of the test to balances with bi-directional output characteristics is discussed. It is also shown how numerical differentiation can be used in order to obtain partial derivatives that are needed for the calculation of the Lipschitz constant. Finally, machine calibration data of NASA's MC60E six-component force balance is selected to demonstrate both implementation and use of the convergence test.

calibration analysis↗

NASA NTRS2000

Dynamic Load-Balancing for Distributed Heterogeneous Computing of Parallel CFD Problems

The developed methodology is aimed at improving the efficiency of executing block-structured algorithms on parallel, distributed, heterogeneous computers. The basic approach of these algorithms is to divide the flow domain into many sub- domains called blocks, and solve the governing equations over these blocks. Dynamic load balancing problem is defined as the efficient distribution of the blocks among the available processors over a period of several hours of computations. In environments with computers of different architecture, operating systems, CPU speed, memory size, load, and network speed, balancing the loads and managing the communication between processors becomes crucial. Load balancing software tools for mutually dependent parallel processes have been created to efficiently utilize an advanced computation environment and algorithms. These tools are dynamic in nature because of the chances in the computer environment during execution time. More recently, these tools were extended to a second operating system: NT. In this paper, the problems associated with this application will be discussed. Also, the developed algorithms were combined with the load sharing capability of LSF to efficiently utilize workstation clusters for parallel computing. Finally, results will be presented on running a NASA based code ADPAC to demonstrate the developed tools for dynamic load balancing.

Ecer, A.↗

NASA NTRS2002

A De-centralized Scheduling and Load Balancing Algorithm for Heterogeneous Grid Environments

In the past two decades, numerous scheduling and load balancing techniques have been proposed for locally distributed multiprocessor systems. However, they all suffer from significant deficiencies when extended to a Grid environment: some use a centralized approach that renders the algorithm unscalable, while others assume the overhead involved in searching for appropriate resources to be negligible. Furthermore, classical scheduling algorithms do not consider a Grid node to be N-resource rich and merely work towards maximizing the utilization of one of the resources. In this paper, we propose a new scheduling and load balancing algorithm for a generalized Grid model of N-resource nodes that not only takes into account the node and network heterogeneity, but also considers the overhead involved in coordinating among the nodes. Our algorithm is decentralized, scalable, and overlaps the node coordination time with that of the actual processing of ready jobs, thus saving valuable clock cycles needed for making decisions. The proposed algorithm is studied by conducting simulations using the Message Passing Interface (MPI) paradigm.

Arora, Manish↗

NASA NTRS2002

A De-Centralized Scheduling and Load Balancing Algorithm for Heterogeneous Grid Environments

In the past two decades, numerous scheduling and load balancing techniques have been proposed for locally distributed multiprocessor systems. However, they all suffer from significant deficiencies when extended to a Grid environment: some use a centralized approach that renders the algorithm unscalable, while others assume the overhead involved in searching for appropriate resources to be negligible. Furthermore, classical scheduling algorithms do not consider a Grid node to be N-resource rich and merely work towards maximizing the utilization of one of the resources. In this paper we propose a new scheduling and load balancing algorithm for a generalized Grid model of N-resource nodes that not only takes into account the node and network heterogeneity, but also considers the overhead involved in coordinating among the nodes. Our algorithm is de-centralized, scalable, and overlaps the node coordination time of the actual processing of ready jobs, thus saving valuable clock cycles needed for making decisions. The proposed algorithm is studied by conducting simulations using the Message Passing Interface (MPI) paradigm.

Arora, Manish↗

NASA NTRS1997

Load Balancing Sequences of Unstructured Adaptive Grids

Mesh adaption is a powerful tool for efficient unstructured grid computations but causes load imbalance on multiprocessor systems. To address this problem, we have developed PLUM, an automatic portable framework for performing adaptive large-scale numerical computations in a message-passing environment. This paper makes several important additions to our previous work. First, a new remapping cost model is presented and empirically validated on an SP2. Next, our load balancing strategy is applied to sequences of dynamically adapted unstructured grids. Results indicate that our framework is effective on many processors for both steady and unsteady problems with several levels of adaption. Additionally, we demonstrate that a coarse starting mesh produces high quality load balancing, at a fraction of the cost required for a fine initial mesh. Finally, we show that the data remapping overhead can be significantly reduced by applying our heuristic processor reassignment algorithm.

Biswas, Rupak↗

NASA NTRS1998

Using Multithreading for the Automatic Load Balancing of 2D Adaptive Finite Element Meshes

In this paper, we present a multi-threaded approach for the automatic load balancing of adaptive finite element (FE) meshes. The platform of our choice is the EARTH multi-threaded system which offers sufficient capabilities to tackle this problem. We implement the question phase of FE applications on triangular meshes, and exploit the EARTH token mechanism to automatically balance the resulting irregular and highly nonuniform workload. We discuss the results of our experiments on EARTH-SP2, an implementation of EARTH on the IBM SP2, with different load balancing strategies that are built into the runtime system.

Heber, Gerd↗

NASA NTRS1998

Using Multi-threading for the Automatic Load Balancing of 2D Adaptive Finite Element Meshes

In this paper, we present a multi-threaded approach for the automatic load balancing of adaptive finite element (FE) meshes The platform of our choice is the EARTH multi-threaded system which offers sufficient capabilities to tackle this problem. We implement the adaption phase of FE applications oil triangular meshes and exploit the EARTH token mechanism to automatically balance the resulting irregular and highly nonuniform workload. We discuss the results of our experiments oil EARTH-SP2, on implementation of EARTH on the IBM SP2 with different load balancing strategies that are built into the runtime system.

Heber, Gerd↗

NASA NTRS1996

Load Balancing Unstructured Adaptive Grids for CFD Problems

Mesh adaption is a powerful tool for efficient unstructured-grid computations but causes load imbalance among processors on a parallel machine. A dynamic load balancing method is presented that balances the workload across all processors with a global view. After each parallel tetrahedral mesh adaption, the method first determines if the new mesh is sufficiently unbalanced to warrant a repartitioning. If so, the adapted mesh is repartitioned, with new partitions assigned to processors so that the redistribution cost is minimized. The new partitions are accepted only if the remapping cost is compensated by the improved load balance. Results indicate that this strategy is effective for large-scale scientific computations on distributed-memory multiprocessors.

Biswas, Rupak↗

NASA NTRS1991

Effects of partitioning and scheduling sparse matrix factorization on communication and load balance

A block based, automatic partitioning and scheduling methodology is presented for sparse matrix factorization on distributed memory systems. Using experimental results, this technique is analyzed for communication and load imbalance overhead. To study the performance effects, these overheads were compared with those obtained from a straightforward 'wrap mapped' column assignment scheme. All experimental results were obtained using test sparse matrices from the Harwell-Boeing data set. The results show that there is a communication and load balance tradeoff. The block based method results in lower communication cost whereas the wrap mapped scheme gives better load balance.

Venugopal, Sesh↗