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1989 International journal of high speed computing  
In fact, all four can be formulated as particular cases of the same totally parallel multilevel algorithm, which we will refer to as TPMA.  ...  In fact, all four can be formulated as particular cases of the same totally parallel multilevel algorithm, which we will refer to as TPMA.  ...  We describe the general algorithm TPMA (Totally Parallel Multilevel Algorithm) in section three, after establishing some notation in section two.  ... 
doi:10.1142/s0129053389000123 fatcat:62ianmje2vc2dk5d7ygwgxzz5u

Mesh Partitioning Algorithm Based on Parallel Finite Element Analysis and Its Actualization

Lei Zhang, Guoxin Zhang, Yi Liu, Hailin Pan
2013 Mathematical Problems in Engineering  
So that it can reduce the application of the threshold of graph partitioning algorithm, improve the calculation efficiency, and promote the application of graph theory and parallel computing.  ...  In parallel computing based on finite element analysis, domain decomposition is a key technique for its preprocessing.  ...  The algorithm actualized in ParMetis is based on parallel multilevel K-path partitioning method, self-adaptive repartitioning algorithm, and parallel multiconstraint algorithm.  ... 
doi:10.1155/2013/751030 fatcat:57pnxoy7s5ealeace3pxj64bfq

Engineering Graph Partitioning Algorithms [chapter]

Vitaly Osipov, Peter Sanders, Christian Schulz
2012 Lecture Notes in Computer Science  
required total node weight of each block ≤ 1 + k total node weight total weight of cut edges as small as possible Applications: various numerical simulations, VLSI design, route planning, . . .  ...  Simulation space is discretized into a mesh Solution of partial differential equations are approximated by linear equations Number of vertices can become quite large → time and memory Parallel processing  ...  + + + Introduction Multilevel Algorithms Coarsening Initial Partitioning Local Improvement Intelligently using multiple runs Parallelization Experiments Discussion Iterated Multilevel [Walshaw  ... 
doi:10.1007/978-3-642-30850-5_3 fatcat:zkee6zsjcjbv7iaxrmjdkocrx4

Scalable Parallel Algorithms for Sparse Linear Systems [chapter]

Anshul Gupta, George Karypis, Vipin Kumar
1997 Applied Optimization  
We have recently developed a parallel formulation of the multilevel graph partitioning algorithm.  ...  Even though these multilevel algorithms are quite fast compared with spectral methods, performing a multilevel partitioning in parallel is desirable for the following reasons.  ... 
doi:10.1007/978-1-4613-3400-2_4 fatcat:ceqkeglhnjexxex4chrt4gldrm

Serial and Parallel Multilevel Graph Partitioning Using Fixed Centers [chapter]

Kayhan Erciyeş, Ali Alp, Geoffrey Marshall
2005 Lecture Notes in Computer Science  
We present new serial and parallel algorithms for multilevel graph partitioning. Our algorithm has coarsening, partitioning and uncoarsening phases like other multilevel partitioning methods.  ...  Using this algorithm, it is possible to obtain theoretically and experimentally much more balanced partitions with substantially decreased total edge costs between the partitions than other algorithms.  ...  In this study, we propose new serial and parallel multilevel algorithms for graph partitioning. We compare these methods with the multilevel graph partitioning method of [10] .  ... 
doi:10.1007/978-3-540-30577-4_16 fatcat:clcjvw2ugjfsnnt77yjaon7nii

Multilevel Diffusion Schemes for Repartitioning of Adaptive Meshes

Kirk Schloegel, George Karypis, Vipin Kumar
1997 Journal of Parallel and Distributed Computing  
In this paper, we present schemes for computing repartitionings of adaptively refined meshes that perform diffusion of vertices in a multilevel framework.  ...  We also show that multilevel diffusion produces results with improved edge-cuts over single-level diffusion, and is better able to make use of heuristics to control the tradeoff between edge-cut and vertex  ...  PARALLEL FORMULATION OF MULTILEVEL DIFFUSION We have implemented the multilevel diffusion algorithms in PARMETIS, which contains a parallel formulation of our multilevel k-way graph partitioning algorithm  ... 
doi:10.1006/jpdc.1997.1410 fatcat:x3e4pha4ufc23obhsokrfkkbye

Space and time efficient implementations of parallel nested dissection

Deganit Armon, John Reif
1992 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures - SPAA '92  
Parallel nested dissection (PND) algorithms, which perform this variable elimination in parallel, have been developed for the PRAM model and for grid architectures.  ...  performed by PND algorithms.  ...  The total work performed in multilevel K j is bounded by the work necessary to eliminate all the separator vertices in the multilevel, multiplied by the number of subgraphs in the multilevel.  ... 
doi:10.1145/140901.141912 dblp:conf/spaa/ArmonR92 fatcat:gmjpqsdiyvgmdoq24zy7eaqdpi

FDPrior: A force-directed based parallel partitioning algorithm for three dimensional integrated circuits on GPGPU

Wan-Jing Chen, Hsien-Kai Kuo, Tsou-Han Chiu, Bo-Cheng Charles Lai
2011 Proceedings of 2011 International Symposium on VLSI Design, Automation and Test  
In recent years, the multilevel hypergraph partitioning algorithms could earn better performances than non-multilevel methods.  ...  Exploiting the algorithmic parallelism on multi-core architectures becomes the key to attain scalable runtime.  ...  In the partitioning filed, multilevel of FM algorithm is a celebrated algorithm [33] . Hence, we organize the multilevel structure of PP3D as the multilevel topology of traditional algorithm.  ... 
doi:10.1109/vdat.2011.5783580 fatcat:uotrz3tyybbyxmtsagov6ntdmm

Parallel multilevel algorithms for hypergraph partitioning

Aleksandar Trifunović, William J. Knottenbelt
2008 Journal of Parallel and Distributed Computing  
In this paper, we present parallel multilevel algorithms for the hypergraph partitioning problem.  ...  Finally, we evaluate the impact of introducing parallel multi-phase refinement into our parallel multilevel algorithm in terms of the trade off between improved partition quality and higher runtime cost  ...  Parallel Multilevel Partitioning Algorithm This section describes our parallel hypergraph partitioning algorithm, based on the multilevel paradigm.  ... 
doi:10.1016/j.jpdc.2007.11.002 fatcat:6dmfuvcw6ffd3ki6yca6lg6wla

Parallel numerical algorithms for optimization of electrical cables

Raim. Èiegis, Rem. Èiegis, M. Meilûnas, G. Jankevièiutë, V. Starikovièius
2008 Mathematical Modelling and Analysis  
Parallel multilevel algorithms are developed using the master-slave and data decomposition paradigms [4] .  ...  Results of computational experiments are presented and the efficiency of the proposed parallel algorithms is investigated.  ...  Parallel multilevel algorithms are developed using the master-slave and data decomposition paradigms [4] .  ... 
doi:10.3846/1392-6292.2008.13.471-482 fatcat:vfcopxuovnahrj2ugnwuqzl3da

Distributed block independent set algorithms and parallel multilevel ILU preconditioners

Chi Shen, Jun Zhang, Kai Wang
2005 Journal of Parallel and Distributed Computing  
Numerical experiments indicate that our domain-based parallel multilevel block ILU preconditioners are robust and efficient.  ...  We present a class of parallel preconditioning strategies utilizing multilevel block incomplete LU (ILU) factorization techniques to solve large sparse linear systems.  ...  One of the most important steps in parallel multilevel block ILU preconditioning techniques is to develop algorithms for constructing BIS efficiently from a distributed sparse matrix.  ... 
doi:10.1016/j.jpdc.2004.10.007 fatcat:blirdwg2jbdkljz2ly6akgjl3u

A multilevel parallel solver for block tridiagonal and banded linear systems

Ibrahim N Hajj, Stig Skelboe
1990 Parallel Computing  
, processor allocation and communication for the multilevel algorithm.  ...  Acknowledgement The careful implementation of the multilevel algorithms together with the numerical ex periments were done by Per Ulkjaer Andersen who also contributed to the principles behind load balancing  ...  The solution algorithm examplified by Fig. 5.2 is applied to a multilevel LU-factorization produced by the parallel multilevel LU-factorization algorithm.  ... 
doi:10.1016/0167-8191(90)90029-9 fatcat:br4wmallv5exhmrdcc5ghzycta

Parallel multilevel k-way partitioning scheme for irregular graphs

George Karypis, Vipin Kumar
1996 Proceedings of the 1996 ACM/IEEE conference on Supercomputing (CDROM) - Supercomputing '96  
In this paper we present a parallel formulation of a multilevel k-way graph partitioning algorithm.  ...  Furthermore, the quality of the partitions produced is comparable (edge-cuts within 5%) to those produced by the serial multilevel k-way algorithm.  ...  Section 2 briefly describes the serial multilevel k-way partitioning algorithm. Section 4 details our parallel formulation of the multilevel k-way partitioning algorithm.  ... 
doi:10.1145/369028.369103 fatcat:fs6spatx6vbcpcvsg5jibkl3my

Partitioning sparse rectangular matrices for parallel computations of Ax and A T v [chapter]

Bruce Hendrickson, Tamara G. Kolda
1998 Lecture Notes in Computer Science  
We then describe how to use (modied) multilevel methods to partition these graphs and how to implement the matrix multiplies in parallel to take advantage of the partitioning.  ...  Finally, we compare various multilevel and other partitioning strategies on matrices from dierent applications. The multilevel methods are shown to be best.  ...  Introduction In many parallel algorithms, we require numerous matrix-vector and matrixtranspose-vector multiplies with sparse matrices.  ... 
doi:10.1007/bfb0095342 fatcat:ffogysqqozh6lf372h4vltinuq

Effective cross-platform, multilevel parallelism via dynamic adaptive execution

W. Ko, M. Yankelevsky, D.S. Nikolopoulos, C.D. Polychronopoulos
2002 Proceedings 16th International Parallel and Distributed Processing Symposium  
This algorithm can be used as a rule of thumb for automatic multilevel parallelization. The effectiveness of the approach is demonstrated on the NAS benchmarks running on two architectural platforms.  ...  This paper presents preliminary efforts to develop compilation and execution environments that achieve performance portability of multilevel parallelization on hierarchical architectures.  ...  The algorithm is executed at runtime, working its way from single-level parallelization to two-level parallelization, three-level parallelization and so on.  ... 
doi:10.1109/ipdps.2002.1016495 dblp:conf/ipps/KoYNP02 fatcat:ge65dyzbvbhzxdt6dhvbagls4a
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