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In this paper, we present a multi-frontal direct solver for one-dimensional isogeometric finite element method. The solver implementation is based on the graph grammar (GG) model. The GG model allows us to express the entire solver algorithm, including generation of frontal matrices, merging, and eliminations as a set of basic undividable tasks called graph grammar productions. Having the solver algorithm expressed as GG productions, we can find the partial order of execution and create adoi:10.7494/csci.2013.14.4.589 fatcat:5kf4gkfbrfddhmsql7jl4sgopq