Multi-Frontal Direct Solver Algorithm for Tri-Diagonal and Block-Diagonal One-Dimensional Problems Derivation of the Linear System for One-Dimensional Finite Difference Method Algebraic Algorithm of the Multi-Frontal Solver Graph-Grammar Based Model of Concurrency of the Multi-Frontal Solver Algorithm One-Dimensional Finite Element Method with Linear Basis Functions One-Dimensional Isogeometric Collocation Method with Quadratic B-Splines One-Dimensional Finite Element Method with Buble Basis Functions One-Dimensional Non-Stationary Problems Euler Scheme with Respect to Time Mixed with Finite Element Method with Linear Basis Functions with Respect to Space α-Scheme with Respect to Time Mixed with Method with Linear Basis Functions for Space Multi-Frontal Direct Solver Algorithm for Multi-Diagonal One-Dimensional Problems One-Dimensional Collocation Method with Higher Order B-Splines One-Dimensional Isogeometric Finite Element Method Multi-Frontal Direct Solver Algorithm for Two-Dimensional Grids with Block Diagonal Structure of the Matrix Two-Dimensional Projection Problem with Linear Basis Functions Two-Dimensional Mesh with Anisotropic Edge Singularity Two-Dimensional Mesh with Point Singularity Multi-Frontal Direct Solver Algorithm for Three-Dimensional Grids with Block Diagonal Structure of the Matrix Three-Dimensional Projection Problem with Linear Basis Functions Three-Dimensional Mesh with Anisotropic Face Singularity Three-Dimensional Mesh with Anisotropic Edge Singularity Three-Dimensional Mesh with Point Singularity Multi-Frontal Direct Solver Algorithm for Two-Dimensional Isogeometric Finite Element Method Isogeometric Finite Element Method for Two-Dimensional Problems Graph-Grammar for Generation of the Elimination Tree Graph-Grammar Productions for the Solver Algorithm Expressing Partial LU Factorization by BLAS Calls LU Factorization of A(1,1) Multiplication of A(1,2) by the Inverse of A(1,1) Multiplication of b(1) by the Inverse of A(1,1) Matrix Multiplication and Subtraction A(2,2)=A(2,2)-A(2,1)A(1,2) Matrix Vector Multiplication and Subtraction b(2)=b,2)-A(2,1)b(1) Example Multi-Frontal Solver Algorithm for Arbitrary Mesh-Based Computations Multi-Frontal Solver Algorithm for Arbitrary Grids Hypermatrix Module Elimination Tree Module Supernodes System Module Interface Structure of Matrices for Different Two-Dimensional Methods Elimination Trees Elimination Trees and Multi-Frontal Solvers Quasi-Optimal Elimination Tree for Two-Dimensional Mesh with Point Singularity Quasi-Optimal Elimination Tree for Two-Dimensional Mesh with Edge Singularity Nested-Dissection Elimination Tree for Two-Dimensional Mesh with Edge Singularity Minimum Degree Tree for Two-Dimensional Mesh with Edge Singularity Estimation of the Number of Floating Point Operations and Memory Usage Elimination Trees for Three-Dimensional Grids Reutilization and Reuse of Partial LU Factorizatons Idea of the Reutilization Algorithm Exemplary Implementation of the Reutilization Algorithm Idea of the Reuse Algorithm Exemplary Implementation of the Reuse Algorithm Numerical Experiments Measuring the Solver Performance by Means of Execution Time Measuring the Solver Performance by Means of the Number of Floating Point Operations (FLOPs) Measuring the Solver Performance by Means of the Efficiency and Speedup Graph-Grammar Based Multi-Thread GALOIS Solver for Two-Dimensional Grids with Singularities Graph-Grammar Based Multi-Thread GALOIS Solver for Three-Dimensional Grids with Singularities Graph-Grammar Based GPU Solver for One-Dimensional Isogoemetric Finite Element Method Graph-Grammar Based GPU Solver for Two-Dimensional Isogoemetric Finite Element Method Graph-Grammar Based Solver for Two-Dimensional Adaptive Finite Element Method Graph-Grammar Based Solver for Three-Dimensional Adaptive Finite Element Method lti-Diagonal One-Dimensional Problems One-Dimensional Collocation Method with Higher Order B-Splines One-Dimensional Isogeometric Finite Element Method Multi-Frontal Direct Solver Algorithm for Two-Dimensional Grids with Block Diagonal Structure of the Matrix Two-Dimensional Projection Problem with Linear Basis Functions Two-Dimensional Mesh with Anisotropic Edge Singularity Two-Dimensional Mesh with Point Singularity Multi-Frontal Direct Solver Algorithm for Three-Dimensional Grids with Block Diagonal Structure of the Matrix Three-Dimensional Projection Problem with Linear Basis Functions Three-Dimensional Mesh with Anisotropic Face Singularity Three-Dimensional Mesh with Anisotropic Edge Singularity Three-Dimensional Mesh with Point Singularity Multi-Frontal Direct Solver Algorithm for Two-Dimensional Isogeometric Finite Element Method Isogeometric Finite Element Method for Two-Dimensional Problems Graph-Grammar for Generation of the Elimination Tree Graph-Grammar Productions for the Solver Algorithm Expressing Partial LU Factorization by BLAS Calls LU Factorization of A(1,1) Multiplication of A(1,2) by the Inverse of A(1,1) Multiplication of b(1) by the Inverse of A(1,1) Matrix Multiplication and Subtraction A(2,2)=A(2,2)-A(2,1)A(1,2) Matrix Vector Multiplication and Subtraction b(2)=b,2)-A(2,1)b(1) Example Multi-Frontal Solver Algorithm for Arbitrary Mesh-Based Computations Multi-Frontal Solver Algorithm for Arbitrary Grids Hypermatrix Module Elimination Tree Module Supernodes System Module Interface Structure of Matrices for Different Two-Dimensional Methods Elimination Trees Elimination Trees and Multi-Frontal Solvers Quasi-Optimal Elimination Tree for Two-Dimensional Mesh with Point Singularity Quasi-Optimal Elimination Tree for Two-Dimensional Mesh with Edge Singularity Nested-Dissection Elimination Tree for Two-Dimensional Mesh with Edge Singularity Minimum Degree Tree for Two-Dimensional Mesh with Edge Singularity Estimation of the Number of Floating Point Operations and Memory Usage Elimination Trees for Three-Dimensional Grids Reutilization and Reuse of Partial LU Factorizatons Idea of the Reutilization Algorithm Exemplary Implementation of the Reutilization Algorithm Idea of the Reuse Algorithm Exemplary Implementation of the Reuse Algorithm Numerical Experiments Measuring the Solver Performance by Means of Execution Time Measuring the Solver Performance by Means of the Number of Floating Point Operations (FLOPs) Measuring the Solver Performance by Means of the Efficiency and Speedup Graph-Grammar Based Multi-Thread GALOIS Solver for Two-Dimensional Grids with Singularities Graph-Grammar Based Multi-Thread GALOIS Solver for Three-Dimensional Grids with Singularities Graph-Grammar Based GPU Solver for One-Dimensional Isogoemetric Finite Element Method Graph-Grammar Based GPU Solver for Two-Dimensional Isogoemetric Finite Element Method Graph-Grammar Based Solver for Two-Dimensional Adaptive Finite Element Method Graph-Grammar Based Solver for Three-Dimensional Adaptive Finite Element Methodrithm for Two-Dimensional Isogeometric Finite Element Method Isogeometric Finite Element Method for Two-Dimensional Problems Graph-Grammar for Generation of the Elimination Tree Graph-Grammar Productions for the Solver Algorithm Expressing Partial LU Factorization by BLAS Calls LU Factorization of A(1,1) Multiplication of A(1,2) by the Inverse of A(1,1) Multiplication of b(1) by the Inverse of A(1,1) Matrix Multiplication and Subtraction A(2,2)=A(2,2)-A(2,1)A(1,2) Matrix Vector Multiplication and Subtraction b(2)=b,2)-A(2,1)b(1) Example Multi-Frontal Solver Algorithm for Arbitrary Mesh-Based Computations Multi-Frontal Solver Algorithm for Arbitrary Grids Hypermatrix Module Elimination Tree Module Supernodes System Module Interface Structure of Matrices for Different Two-Dimensional Methods Elimination Trees Elimination Trees and Multi-Frontal Solvers Quasi-Optimal Elimination Tree for Two-Dimensional Mesh with Point Singularity Quasi-Optimal Elimination Tree for Two-Dimensional Mesh with Edge Singularity Nested-Dissection Elimination Tree for Two-Dimensional Mesh with Edge Singularity Minimum Degree Tree for Two-Dimensional Mesh with Edge Singularity Estimation of the Number of Floating Point Operations and Memory Usage Elimination Trees for Three-Dimensional Grids Reutilization and Reuse of Partial LU Factorizatons Idea of the Reutilization Algorithm Exemplary Implementation of the Reutilization Algorithm Idea of the Reuse Algorithm Exemplary Implementation of the Reuse Algorithm Numerical Experiments Measuring the Solver Performance by Means of Execution Time Measuring the Solver Performance by Means of the Number of Floating Point Operations (FLOPs) Measuring the Solver Performance by Means of the Efficiency and Speedup Graph-Grammar Based Multi-Thread GALOIS Solver for Two-Dimensi.