The Experts below are selected from a list of 195 Experts worldwide ranked by ideXlab platform
Tomislav Jarak - One of the best experts on this subject based on the ideXlab platform.
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Mixed meshless local Petrov–Galerkin collocation method for modeling of material discontinuity
Computational Mechanics, 2017Co-Authors: Boris Jalušić, Jurica Sorić, Tomislav JarakAbstract:A mixed meshless local Petrov–Galerkin (MLPG) collocation method is proposed for solving the two-dimensional boundary value problem of heterogeneous structures. The heterogeneous structures are defined by partitioning the total material domain into subdomains with different linear-elastic isotropic properties which define homogeneous materials. The discretization and approximation of unknown field variables is done for each homogeneous material independently, therein the interface of the homogeneous materials is discretized with overlapping nodes. For the approximation, the moving least square method with the imposed Interpolation Condition is utilized. The solution for the entire heterogeneous structure is obtained by enforcing displacement continuity and traction reciprocity Conditions at the nodes representing the interface boundary. The accuracy and numerical efficiency of the proposed mixed MLPG collocation method is demonstrated by numerical examples. The obtained results are compared with a standard fully displacement (primal) meshless approach as well as with available analytical and numerical solutions. Excellent agreement of the solutions is exhibited and a more robust, superior and stable modeling of material discontinuity is achieved using the mixed method.
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Mixed meshless local Petrov---Galerkin collocation method for modeling of material discontinuity
Computational Mechanics, 2016Co-Authors: Boris Jalušić, Jurica Sorić, Tomislav JarakAbstract:A mixed meshless local Petrov---Galerkin (MLPG) collocation method is proposed for solving the two-dimensional boundary value problem of heterogeneous structures. The heterogeneous structures are defined by partitioning the total material domain into subdomains with different linear-elastic isotropic properties which define homogeneous materials. The discretization and approximation of unknown field variables is done for each homogeneous material independently, therein the interface of the homogeneous materials is discretized with overlapping nodes. For the approximation, the moving least square method with the imposed Interpolation Condition is utilized. The solution for the entire heterogeneous structure is obtained by enforcing displacement continuity and traction reciprocity Conditions at the nodes representing the interface boundary. The accuracy and numerical efficiency of the proposed mixed MLPG collocation method is demonstrated by numerical examples. The obtained results are compared with a standard fully displacement (primal) meshless approach as well as with available analytical and numerical solutions. Excellent agreement of the solutions is exhibited and a more robust, superior and stable modeling of material discontinuity is achieved using the mixed method.
Boris Jalušić - One of the best experts on this subject based on the ideXlab platform.
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Mixed meshless local Petrov–Galerkin collocation method for modeling of material discontinuity
Computational Mechanics, 2017Co-Authors: Boris Jalušić, Jurica Sorić, Tomislav JarakAbstract:A mixed meshless local Petrov–Galerkin (MLPG) collocation method is proposed for solving the two-dimensional boundary value problem of heterogeneous structures. The heterogeneous structures are defined by partitioning the total material domain into subdomains with different linear-elastic isotropic properties which define homogeneous materials. The discretization and approximation of unknown field variables is done for each homogeneous material independently, therein the interface of the homogeneous materials is discretized with overlapping nodes. For the approximation, the moving least square method with the imposed Interpolation Condition is utilized. The solution for the entire heterogeneous structure is obtained by enforcing displacement continuity and traction reciprocity Conditions at the nodes representing the interface boundary. The accuracy and numerical efficiency of the proposed mixed MLPG collocation method is demonstrated by numerical examples. The obtained results are compared with a standard fully displacement (primal) meshless approach as well as with available analytical and numerical solutions. Excellent agreement of the solutions is exhibited and a more robust, superior and stable modeling of material discontinuity is achieved using the mixed method.
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Mixed meshless local Petrov---Galerkin collocation method for modeling of material discontinuity
Computational Mechanics, 2016Co-Authors: Boris Jalušić, Jurica Sorić, Tomislav JarakAbstract:A mixed meshless local Petrov---Galerkin (MLPG) collocation method is proposed for solving the two-dimensional boundary value problem of heterogeneous structures. The heterogeneous structures are defined by partitioning the total material domain into subdomains with different linear-elastic isotropic properties which define homogeneous materials. The discretization and approximation of unknown field variables is done for each homogeneous material independently, therein the interface of the homogeneous materials is discretized with overlapping nodes. For the approximation, the moving least square method with the imposed Interpolation Condition is utilized. The solution for the entire heterogeneous structure is obtained by enforcing displacement continuity and traction reciprocity Conditions at the nodes representing the interface boundary. The accuracy and numerical efficiency of the proposed mixed MLPG collocation method is demonstrated by numerical examples. The obtained results are compared with a standard fully displacement (primal) meshless approach as well as with available analytical and numerical solutions. Excellent agreement of the solutions is exhibited and a more robust, superior and stable modeling of material discontinuity is achieved using the mixed method.
François Dubois - One of the best experts on this subject based on the ideXlab platform.
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Finite volumes and mixed Petrov-Galerkin finite elements : the unidimensional problem
arXiv: Numerical Analysis, 2014Co-Authors: François DuboisAbstract:For Laplace operator in one space dimension, we propose to formulate the heuristic finite volume method with the help of mixed Petrov-Galerkin finite elements. Weighting functions for gradient discretization are parameterized by some universal function. We propose for this function a compatibility Interpolation Condition and we prove that such a Condition is equivalent to the inf-sup property when studying stability of the numerical scheme. In the case of stable scheme and under two distinct hypotheses concerning the regularity of the solution, we demonstrate convergence of the finite volume method in appropriate Hilbert spaces and with optimal order of accuracy.
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Finite volumes and mixed Petrov‐Galerkin finite elements: The unidimensional problem
Numerical Methods for Partial Differential Equations, 2000Co-Authors: François DuboisAbstract:For Laplace operator in one space dimension, we propose to formulate the heuristic finite volume method with the help of mixed Petrov-Galerkin finite elements. Weighting functions for gradient discretization are parameterized by some function ψ : [0, 1] ℝ. We propose for this function ψ a compatibility Interpolation Condition, and we prove that such a Condition is equivalent to the inf-sup property when studying stability of the numerical scheme. In the case of stable scheme and under two distinct hypotheses concerning the regularity of the solution, we demonstrate convergence of the finite volume method in appropriate Hilbert spaces and with optimal order of accuracy. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 335–360, 2000
Irina Perfilieva - One of the best experts on this subject based on the ideXlab platform.
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closeness in similarity based reasoning with an Interpolation Condition
Fuzzy Sets and Systems, 2016Co-Authors: Irina PerfilievaAbstract:This study considers an approximate reasoning scheme where the knowledge base is a set of fuzzy IF-THEN rules and the inference mechanism is characterized in terms of closeness. We propose the interpretation of this scheme, which uses Ruspini's theory of Conditional consistency and implication measures, and its adaptation to fuzzy sets. In the proposed interpretation, we find the necessary and sufficient Conditions to ensure that the computation of the conclusion fulfills the Interpolation Condition. We show that the inference mechanism is equivalent to the compositional rule of inference in the form of inf ? ? composition. Finally, we construct a particular interpretation where all of the considered requirements are satisfied and the inference operator reduces to a piecewise linear Interpolation function.
Jurica Sorić - One of the best experts on this subject based on the ideXlab platform.
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Mixed meshless local Petrov–Galerkin collocation method for modeling of material discontinuity
Computational Mechanics, 2017Co-Authors: Boris Jalušić, Jurica Sorić, Tomislav JarakAbstract:A mixed meshless local Petrov–Galerkin (MLPG) collocation method is proposed for solving the two-dimensional boundary value problem of heterogeneous structures. The heterogeneous structures are defined by partitioning the total material domain into subdomains with different linear-elastic isotropic properties which define homogeneous materials. The discretization and approximation of unknown field variables is done for each homogeneous material independently, therein the interface of the homogeneous materials is discretized with overlapping nodes. For the approximation, the moving least square method with the imposed Interpolation Condition is utilized. The solution for the entire heterogeneous structure is obtained by enforcing displacement continuity and traction reciprocity Conditions at the nodes representing the interface boundary. The accuracy and numerical efficiency of the proposed mixed MLPG collocation method is demonstrated by numerical examples. The obtained results are compared with a standard fully displacement (primal) meshless approach as well as with available analytical and numerical solutions. Excellent agreement of the solutions is exhibited and a more robust, superior and stable modeling of material discontinuity is achieved using the mixed method.
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Mixed meshless local Petrov---Galerkin collocation method for modeling of material discontinuity
Computational Mechanics, 2016Co-Authors: Boris Jalušić, Jurica Sorić, Tomislav JarakAbstract:A mixed meshless local Petrov---Galerkin (MLPG) collocation method is proposed for solving the two-dimensional boundary value problem of heterogeneous structures. The heterogeneous structures are defined by partitioning the total material domain into subdomains with different linear-elastic isotropic properties which define homogeneous materials. The discretization and approximation of unknown field variables is done for each homogeneous material independently, therein the interface of the homogeneous materials is discretized with overlapping nodes. For the approximation, the moving least square method with the imposed Interpolation Condition is utilized. The solution for the entire heterogeneous structure is obtained by enforcing displacement continuity and traction reciprocity Conditions at the nodes representing the interface boundary. The accuracy and numerical efficiency of the proposed mixed MLPG collocation method is demonstrated by numerical examples. The obtained results are compared with a standard fully displacement (primal) meshless approach as well as with available analytical and numerical solutions. Excellent agreement of the solutions is exhibited and a more robust, superior and stable modeling of material discontinuity is achieved using the mixed method.
