The Experts below are selected from a list of 5394 Experts worldwide ranked by ideXlab platform
Carlo Cattani - One of the best experts on this subject based on the ideXlab platform.
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a computational method for solving stochastic ito volterra integral equations based on stochastic operational matrix for generalized hat basis functions
Journal of Computational Physics, 2014Co-Authors: M H Heydari, M R Hooshmandasl, F Maalek M Ghaini, Carlo CattaniAbstract:Abstract In this paper, a new computational method based on the generalized hat basis functions is proposed for solving stochastic Ito–Volterra integral equations. In this way, a new stochastic operational matrix for generalized hat functions on the finite interval [ 0 , T ] is obtained. By using these basis functions and their stochastic operational matrix, such problems can be transformed into linear lower triangular systems of algebraic equations which can be directly solved by Forward Substitution. Also, the rate of convergence of the proposed method is considered and it has been shown that it is O ( 1 n 2 ) . Further, in order to show the accuracy and reliability of the proposed method, the new approach is compared with the block pulse functions method by some examples. The obtained results reveal that the proposed method is more accurate and efficient in comparison with the block pule functions method.
M H Heydari - One of the best experts on this subject based on the ideXlab platform.
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a computational method for solving stochastic ito volterra integral equations based on stochastic operational matrix for generalized hat basis functions
Journal of Computational Physics, 2014Co-Authors: M H Heydari, M R Hooshmandasl, F Maalek M Ghaini, Carlo CattaniAbstract:Abstract In this paper, a new computational method based on the generalized hat basis functions is proposed for solving stochastic Ito–Volterra integral equations. In this way, a new stochastic operational matrix for generalized hat functions on the finite interval [ 0 , T ] is obtained. By using these basis functions and their stochastic operational matrix, such problems can be transformed into linear lower triangular systems of algebraic equations which can be directly solved by Forward Substitution. Also, the rate of convergence of the proposed method is considered and it has been shown that it is O ( 1 n 2 ) . Further, in order to show the accuracy and reliability of the proposed method, the new approach is compared with the block pulse functions method by some examples. The obtained results reveal that the proposed method is more accurate and efficient in comparison with the block pule functions method.
Andres M Aguirremesa - One of the best experts on this subject based on the ideXlab platform.
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a block Forward Substitution method for solving the hypercomplex finite element system of equations
Computer Methods in Applied Mechanics and Engineering, 2021Co-Authors: Andres M Aguirremesa, Manuel J Garcia, Mauricio Aristizabal, David Wagner, Daniel Ramireztamayo, Arturo Montoya, Harry R MillwaterAbstract:Abstract The hypercomplex finite element method, ZFEM, allows the analyst to compute highly-accurate arbitrary-order shape, material property, and loading derivatives by augmenting the traditional finite element method with multiple imaginary degrees of freedom. In ZFEM, the real variables are converted to hypercomplex variables such as multicomplex, multidual, or quaternions. By uplifting the real variables to hypercomplex, derivatives are computed in an automated fashion using a standard finite element formulation. The use of multicomplex or multidual numbers provides higher-order derivatives. The drawback of ZFEM is that it increases the number of degrees of freedom of the real variable system by a factor 2 n , where n is the order of the required derivative. In consequence, ZFEM increases the memory consumption and the solution time of the system of equations compared to the real variable system. The block Forward Substitution method (BFS), proposed in this work, addresses the memory and runtime issues. This new method solves the original real-valued FEM system once. Then, the derivatives are computed using pseudo-loads with the original system of equations. In contrast with the conventional solution method of ZFEM, BFS computes the hypercomplex contributions to the stiffness matrix element-wise, and it never assembles nor solves the full hypercomplex system of equations. In effect, the BFS method generalizes the first-order semi-analytical complex variable method to any order derivative. The BFS method provides the capability to allow a combination of real-variable and hypercomplex-variable elements within the same model. The numerical results indicate that a first-order derivative can be obtained with 1% to 8% additional computational time of the real-variable analysis. This allows the computation of multiple first-order derivatives by post-processing of a single FEM analysis. Additionally, it was shown that fourth-order shape sensitivities can be computed in less than 5% additional runtime of the real-variable FEM analysis.
M Rostami - One of the best experts on this subject based on the ideXlab platform.
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numerical approach for solving stochastic volterra fredholm integral equations by stochastic operational matrix
Computers & Mathematics With Applications, 2012Co-Authors: Morteza Khodabin, K Maleknejad, M Rostami, Mahdi NouriAbstract:In this paper, we obtain stochastic operational matrix of block pulse functions on interval [0,1) to solve stochastic Volterra-Fredholm integral equations. By using block pulse functions and their stochastic operational matrix of integration, the stochastic Volterra-Fredholm integral equation can be reduced to a linear lower triangular system which can be directly solved by Forward Substitution. We prove that the rate of convergence is O(h). Furthermore, the results show that the approximate solutions have a good degree of accuracy.
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numerical solution of stochastic volterra integral equations by a stochastic operational matrix based on block pulse functions
Mathematical and Computer Modelling, 2012Co-Authors: K Maleknejad, Morteza Khodabin, M RostamiAbstract:Abstract This article proposes an efficient method for solving stochastic Volterra integral equations. By using block pulse functions and their stochastic operational matrix of integration, a stochastic Volterra integral equation can be reduced to a linear lower triangular system, which can be directly solved by Forward Substitution. The results show that the approximate solutions have a good degree of accuracy.
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a numerical method for solving m dimensional stochastic ito volterra integral equations by stochastic operational matrix
Computers & Mathematics With Applications, 2012Co-Authors: K Maleknejad, Morteza Khodabin, M RostamiAbstract:The multidimensional Ito-Volterra integral equations arise in many problems such as an exponential population growth model with several independent white noise sources. In this paper, we obtain a stochastic operational matrix of block pulse functions on interval [0,1) to solve m-dimensional stochastic Ito-Volterra integral equations. By using block pulse functions and their stochastic operational matrix of integration, m-dimensional stochastic Ito-Volterra integral equations can be reduced to a linear lower triangular system which can be directly solved by Forward Substitution. We prove that the rate of convergence is O(h). Furthermore, a 95% confidence interval of the errors' mean is made, the results shows that the approximate solutions have a credible degree of accuracy.
Harry R Millwater - One of the best experts on this subject based on the ideXlab platform.
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a block Forward Substitution method for solving the hypercomplex finite element system of equations
Computer Methods in Applied Mechanics and Engineering, 2021Co-Authors: Andres M Aguirremesa, Manuel J Garcia, Mauricio Aristizabal, David Wagner, Daniel Ramireztamayo, Arturo Montoya, Harry R MillwaterAbstract:Abstract The hypercomplex finite element method, ZFEM, allows the analyst to compute highly-accurate arbitrary-order shape, material property, and loading derivatives by augmenting the traditional finite element method with multiple imaginary degrees of freedom. In ZFEM, the real variables are converted to hypercomplex variables such as multicomplex, multidual, or quaternions. By uplifting the real variables to hypercomplex, derivatives are computed in an automated fashion using a standard finite element formulation. The use of multicomplex or multidual numbers provides higher-order derivatives. The drawback of ZFEM is that it increases the number of degrees of freedom of the real variable system by a factor 2 n , where n is the order of the required derivative. In consequence, ZFEM increases the memory consumption and the solution time of the system of equations compared to the real variable system. The block Forward Substitution method (BFS), proposed in this work, addresses the memory and runtime issues. This new method solves the original real-valued FEM system once. Then, the derivatives are computed using pseudo-loads with the original system of equations. In contrast with the conventional solution method of ZFEM, BFS computes the hypercomplex contributions to the stiffness matrix element-wise, and it never assembles nor solves the full hypercomplex system of equations. In effect, the BFS method generalizes the first-order semi-analytical complex variable method to any order derivative. The BFS method provides the capability to allow a combination of real-variable and hypercomplex-variable elements within the same model. The numerical results indicate that a first-order derivative can be obtained with 1% to 8% additional computational time of the real-variable analysis. This allows the computation of multiple first-order derivatives by post-processing of a single FEM analysis. Additionally, it was shown that fourth-order shape sensitivities can be computed in less than 5% additional runtime of the real-variable FEM analysis.