A review of block Krylov subspace methods for multisource electromagnetic modelling

Puzyrev, Vladimir; María, José

doi:10.1093/gji/ggv216

Cited by 34 publications

(18 citation statements)

References 46 publications

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“…As a consequence of the problems related to strong scalability, parallel applications may not always make an efficient use of all the available cores, both in terms of time reduction and energy consumption. Therefore, using all the available cores may not necessarily be better (as expected) than using half of them (some examples of this behavior can be found in [23,24]). In addition, as performance can depend on the mapping, providing resilience is a useful way to take advantage of the available resources.…”

Section: Error Detection With Notificationmentioning

confidence: 88%

Soft errors detection and automatic recovery based on replication combined with different levels of checkpointing

Montezanti

Rucci

Giusti

et al. 2020

Future Generation Computer Systems

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Handling faults is a growing concern in HPC. In future exascale systems, it is projected that silent undetected errors will occur several times a day, increasing the occurrence of corrupted results. In this article, we propose SEDAR, which is a methodology that improves system reliability against transient faults when running parallel message-passing applications. Our approach, based on process replication for detection, combined with different levels of checkpointing for automatic recovery, has the goal of helping users of scientific applications to obtain executions with correct results. SEDAR is structured in three levels: (1) only detection and safestop with notification; (2) recovery based on multiple system-level checkpoints; and (3) recovery based on a single valid user-level checkpoint. As each of these variants supplies a particular coverage but involves limitations and implementation costs, SEDAR can be adapted to the needs of the system. In this work, a description of the methodology is presented and the temporal behavior of employing each SEDAR strategy is mathematically described, both in the absence and presence of faults. A model that considers all the fault scenarios on a test application is introduced to show the validity of the detection and recovery mechanisms. An overhead evaluation of each variant is performed with applications involving different communication patterns; this is also used to extract guidelines about when it is beneficial to employ each SEDAR protection level. As a result, we show its efficacy and viability to tolerate transient faults in target HPC environments.

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Section: Error Detection With Notificationmentioning

confidence: 88%

Soft errors detection and automatic recovery based on replication combined with different levels of checkpointing

Montezanti

Rucci

Giusti

et al. 2020

Future Generation Computer Systems

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“…In this case, the task is simplified and can be solved by means of block versions of Krylov-type iterative methods. To solve sparse matrices, there are the following methods: block BiCGStab, block GMRES, GL-LSQR, MHGMRES(m), MEGCR, and others [8]. Typically, if an effective preconditioner is used, block methods are preferred rather than solving linear systems sequentially with different right-hand sides.…”

Section: Approaches To Solving the Sequence Of Linear Systemsmentioning

confidence: 99%

Choosing order of operations to accelerate strip structure analysis in parameter range

Kuksenko

Akhunov

Gazizov

2018

J. Phys.: Conf. Ser.

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Abstract. The paper considers the issue of using iteration methods in solving the sequence of linear algebraic systems obtained in quasistatic analysis of strip structures with the method of moments. Using the analysis of 4 strip structures, the authors have proved that additional acceleration (up to 2.21 times) of the iterative process can be obtained during the process of solving linear systems repeatedly by means of choosing a proper order of operations and a preconditioner. The obtained results can be used to accelerate the process of computer-aided design of various strip structures. The choice of the order of operations to accelerate the process is quite simple, universal and could be used not only for strip structure analysis but also for a wide range of computational problems. IntroductionDistributed circuits based on various strip structures are widely used in radioelectronic equipment, both as transmission lines that maintain proper characteristics for desired signals for a long time and as a basis for new protective devices. A strip structure consists of signal and ground conductors and a dielectric substrate. The separation between conductors, their thickness, other geometrical parameters and dielectric permittivity of a substrate can be repeatedly changed during simulation and optimization of elements and devices. These processes significantly increase computational costs. Generally, hardware accelerators (multicore workstations, clusters, graphical processing units) are used to decrease computational costs, while algorithmic methods are often ignored. A quasistatic approach, which is based on calculating electric capacitance with the method of moments [1], is widely used to decrease computational costs of strip structure analysis in contrast to the electrodynamic approach. The method of moments implies solving linear systems with dense matrix. This paper presents the research into application of iterative methods for solving dense linear systems repeatedly during multivariant analysis of strip structures using the method of moments with the optimal choice of order of operations.

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“…M8 is also a challenging example for direct solvers whose condition number cannot be even estimated with high degree of confidence, so we provided an approximate value. Both these matrices are built from the complex model shown in Figure 6 of Puzyrev and Cela (2015). The original model was modified to accommodate up to 1000 receiver positions and to have higher conductivity contrasts, anisotropy factor of up to 10 and air conductivity of 10 -10 S/m.…”

Section: Test Matricesmentioning

confidence: 99%

Evaluation of parallel direct sparse linear solvers in electromagnetic geophysical problems

Puzyrev

Korić

Wilkin

2016

Computers & Geosciences

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High performance computing is absolutely necessary for large-scale geophysical simulations. In order to obtain a realistic image of a geologically complex area, industrial surveys collect vast amounts of data making the computational cost extremely high for the subsequent simulations. A major computational bottleneck of modeling and inversion algorithms is solving the large sparse systems of linear ill-conditioned equations in complex domains with multiple right hand sides. Recently, parallel direct solvers have been successfully applied to multi-source seismic and electromagnetic problems. These methods are robust and exhibit good performance, but often require large amounts of memory and have limited scalability. In this paper, we evaluate modern direct solvers on large-scale modeling examples that previously were considered unachievable with these methods. Performance and scalability tests utilizing up to 65,536 cores on the Blue Waters supercomputer clearly illustrate the robustness, efficiency and competitiveness of direct solvers compared to iterative techniques. Wide use of direct methods utilizing modern parallel architectures will allow modeling tools to accurately support multi-source surveys and 3D data acquisition geometries, thus promoting a more efficient use of the electromagnetic methods in geophysics.The authors would like to thank the MUMPS and PARDISO developers for providing free academic licenses and Dr. Anshul Gupta for access to his solver library which is not publicly available. We also would like to thank the Private Sector Program and the Blue Waters sustained-petascale computing project at the\ud National Center for Supercomputing Applications (NCSA), which is supported by the National Science Foundation (awards OCI-\ud 0725070 and ACI-1238993) and the state of Illinois. The shared-memory tests were performed on the MareNostrum supercomputer of the Barcelona Supercomputer Center. The first author\ud acknowledges funding from the Repsol-BSC Research Center through the AURORA project and support from the RISE Horizon 2020 European Project GEAGAM (644602). The authors wish to thank Jef Caers and two anonymous reviewers for their valuable\ud comments that significantly helped to improve this paper.Peer ReviewedPostprint (author's final draft

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A review of block Krylov subspace methods for multisource electromagnetic modelling

Cited by 34 publications

References 46 publications

Soft errors detection and automatic recovery based on replication combined with different levels of checkpointing

Soft errors detection and automatic recovery based on replication combined with different levels of checkpointing

Choosing order of operations to accelerate strip structure analysis in parameter range

Evaluation of parallel direct sparse linear solvers in electromagnetic geophysical problems

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