Parallel Performance of Multithreaded ICCG Solver Based on Algebraic Block Multicolor Ordering in Finite Element Electromagnetic Field Analyses

Fast Computation of Linear Systems Based on Parallelized Preconditioned MRTR Method Supported by Block‐Multicolor Ordering in Electromagnetic Field Analysis Using Edge‐Based Finite Element Method

“…At first, Fig. shows the nonzero distributions after ordering, where MC is a technique that each of nodes is colored by Greedy technique , and BCM is a technique that the number of unknown variables ( s ) is set in block and then block is colored. At BMC, larger parameter s is desirable from the point of convergence performance, but it is possible that some problems make the number of colors increase, so that parallelization is deteriorated.…”

“…At numerical analysis using nonstructural lattice such as finite element method, the block‐multicolor (BMC) ordering proposed by Iwashita and colleagues can realize parallelization of preconditioning part. The effectiveness of this technique is discussed mathematically based on fill‐in arising at incomplete Cholesky decomposition, where application to magnetic field analysis is reported . Meanwhile, the number of unknown parameters included in each block is added as parameter, so that parallel performance is likely to be deteriorated according to these values.…”

Algebraic Block Multi-Color Ordering Method for Parallel Multi-Threaded Sparse Triangular Solver in ICCG Method

“…Typical examples are hierarchical interface decomposition (HID) [42] and heuristics for nodal or block multi-coloring [13][14][15]. These techniques and other related methods have been used in various application domains, such as CFD, computational electromagnetics, and structure analyses [16,17,[43][44][45].…”

“…Following on from these research activities, the algebraic block multi-color ordering method was introduced for a general sparse linear system in [13]. Although there are various options for coloring or blocking methods [14,15], this technique has been used in various applications because of its advantages in terms of convergence, data locality, and the number of synchronizations [16,17]. Particularly, several high-performance implementations of the HPCG benchmark adopt the technique, which shows the effectiveness of the method in a fast multigrid solver with the parallel GS smoother [18][19][20][21][22].…”

Enhancement of Algebraic Block Multi-Color Ordering for ILU Preconditioning and Its Performance Evaluation in Preconditioned GMRES Solver

“…Considering the advantages of the block multi-color ordering method, Iwashita et al developed its algebraic version that can be applied to a general linear system arising in unstructured problems [11]. The algebraic block multi-color ordering (ABMC) method has discovered its effectiveness in a multi-threaded ICCG (Incomplete Cholesky Conjugate Gradient) solver [12] and has also been used for high performance implementation of HPCG benchmark programs [13]. In these research activities, this method has been mainly discussed in symmetric coefficient matrix cases.…”