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.