TY - GEN
T1 - Graph grammar based parallel direct solver for 1D and 2D isogeometric finite element method
AU - Paszyński, MacIej R.
AU - Kuźnik, Krzysztof M.
AU - Calo, Victor M.
PY - 2012
Y1 - 2012
N2 - In this paper we present a multi-frontal direct solver algorithm for one and two dimensional isogeometric finite element method. The solver algorithm is tested on heat transfer model problem. The algorithm is partitioned into basic undividable tasks calling graph grammar productions, responsible for generation of the merging and elimination pattern, as well as processing multiple frontal matrices during the computation process. The productions are scheduled into nodes of the GPU graphic card and executed in concurrent. The paper is concluded with numerical results concerning the execution of the solver algorithm on GeForce GTX 260 device in one dimension, delivering O(logN) execution time for linear, quadratic, cubic and higher order B-splines, as well as on NVidia Tesla C2070 device in two dimension, delivering O(NlogN) computational cost for linear, quadratic and cubic B-splines.
AB - In this paper we present a multi-frontal direct solver algorithm for one and two dimensional isogeometric finite element method. The solver algorithm is tested on heat transfer model problem. The algorithm is partitioned into basic undividable tasks calling graph grammar productions, responsible for generation of the merging and elimination pattern, as well as processing multiple frontal matrices during the computation process. The productions are scheduled into nodes of the GPU graphic card and executed in concurrent. The paper is concluded with numerical results concerning the execution of the solver algorithm on GeForce GTX 260 device in one dimension, delivering O(logN) execution time for linear, quadratic, cubic and higher order B-splines, as well as on NVidia Tesla C2070 device in two dimension, delivering O(NlogN) computational cost for linear, quadratic and cubic B-splines.
KW - Graph grammar
KW - Isogeometric finite element method
KW - Models of concurrency
KW - Parallel direct solvers
UR - http://www.scopus.com/inward/record.url?scp=84871630246&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:84871630246
SN - 9783950353709
T3 - ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers
SP - 849
EP - 858
BT - ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers
T2 - 6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012
Y2 - 10 September 2012 through 14 September 2012
ER -