The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
Frans P. Van Der Meer - One of the best experts on this subject based on the ideXlab platform.
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Stress‐controlled weakly Periodic Boundary conditions: Axial stress under varying orientations
International Journal for Numerical Methods in Engineering, 2020Co-Authors: Erik Giesen Loo, Frans P. Van Der MeerAbstract:The accuracy of multiscale modeling approaches for the analysis of heterogeneous materials hinges on the representativeness of the micromodel. One of the issues that affects this representativeness is the application of appropriate Boundary conditions. Periodic Boundary conditions are the most common choice. However, when localization takes place, Periodic Boundary conditions tend to overconstrain the microscopic problem. Weakly Periodic Boundary conditions have been proposed to overcome this effect. In this study, the effectiveness of weakly Periodic Boundary conditions in restoring transverse isotropy of representative volume elements (RVE) for a fiber-reinforced composite with elastoplastic matrix is investigated. The formulation of weakly Periodic Boundary conditions is extended to allow for force-controlled simulations where a uniaxial stress can be applied. A series of simulations is performed where the orientation of applied stress is gradually varied and the influence of this orientation on the averaged response is examined. An original method is presented to test the correlation between the ultimate principal stress and average localization angle of shear bands within an RVE. It is concluded that weakly Periodic Boundary conditions alleviate anisotropy in the RVE response but do not remove it.
Hans Gerd Evertz - One of the best experts on this subject based on the ideXlab platform.
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Efficient matrix-product state method for Periodic Boundary conditions
Physical Review B, 2010Co-Authors: Peter Pippan, Steven R. White, Hans Gerd EvertzAbstract:We introduce an efficient method to calculate the ground state of one-dimensional lattice models with Periodic Boundary conditions. The method works in the representation of Matrix Product States (MPS), related to the Density Matrix Renormalization Group (DMRG) method. It improves on a previous approach by Verstraete et al. We introduce a factorization procedure for long products of MPS matrices, which reduces the computational effort from m^5 to m^3, where m is the matrix dimension, and m ~ 100 - 1000 in typical cases. We test the method on the S=1/2 and S=1 Heisenberg chains. It is also applicable to non-translationally invariant cases. The new method makes ground state calculations with Periodic Boundary conditions about as efficient as traditional DMRG calculations for systems with open boundaries.
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efficient matrix product state method for Periodic Boundary conditions
Physical Review B, 2010Co-Authors: Peter Pippan, Steven R. White, Hans Gerd EvertzAbstract:We introduce an efficient method to calculate the ground state of one-dimensional lattice models with Periodic Boundary conditions. The method works in the representation of matrix product states (MPS), related to the density matrix renormalization group (DMRG) method. It improves on a previous approach by Verstraete et al. We introduce a factorization procedure for long products of MPS matrices, which reduces the computational effort from ${m}^{5}$ to ${m}^{3}$, where $m$ is the matrix dimension, and $m\ensuremath{\simeq}100--1000$ in typical cases. We test the method on the $S=\frac{1}{2}$ and $S=1$ Heisenberg chains. It is also applicable to nontranslationally invariant cases. The method makes ground-state calculations with Periodic Boundary conditions about as efficient as traditional DMRG calculations for systems with open boundaries.
A.s. Vatsala - One of the best experts on this subject based on the ideXlab platform.
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Monotone iterative technique for fractional differential equations with Periodic Boundary conditions
Opuscula Mathematica, 2009Co-Authors: Josimar Ramirez, A.s. VatsalaAbstract:In this paper we develop Monotone Method using upper and lower solutions for fractional differential equations with Periodic Boundary conditions. Initially we develop a comparison result and prove that the solution of the linear fractional differential equation with Periodic Boundary condition exists and is unique. Using this we develop iterates which converge uniformly monotonically to minimal and maximal solutions of the nonlinear fractional differential equations with Periodic Boundary conditions in the weighted norm.
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Periodic Boundary value problems of impulsive differential equations
Applicable Analysis, 1992Co-Authors: A.s. Vatsala, Yong SunAbstract:Periodic Boundary value problems of impulsive differential equations with continuous or discontinuous right hand side will be studied by comparis-ing theorems and operator theory. Both existence and bounds of solutions will be obtained.
Erik Giesen Loo - One of the best experts on this subject based on the ideXlab platform.
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Stress‐controlled weakly Periodic Boundary conditions: Axial stress under varying orientations
International Journal for Numerical Methods in Engineering, 2020Co-Authors: Erik Giesen Loo, Frans P. Van Der MeerAbstract:The accuracy of multiscale modeling approaches for the analysis of heterogeneous materials hinges on the representativeness of the micromodel. One of the issues that affects this representativeness is the application of appropriate Boundary conditions. Periodic Boundary conditions are the most common choice. However, when localization takes place, Periodic Boundary conditions tend to overconstrain the microscopic problem. Weakly Periodic Boundary conditions have been proposed to overcome this effect. In this study, the effectiveness of weakly Periodic Boundary conditions in restoring transverse isotropy of representative volume elements (RVE) for a fiber-reinforced composite with elastoplastic matrix is investigated. The formulation of weakly Periodic Boundary conditions is extended to allow for force-controlled simulations where a uniaxial stress can be applied. A series of simulations is performed where the orientation of applied stress is gradually varied and the influence of this orientation on the averaged response is examined. An original method is presented to test the correlation between the ultimate principal stress and average localization angle of shear bands within an RVE. It is concluded that weakly Periodic Boundary conditions alleviate anisotropy in the RVE response but do not remove it.
Peter Pippan - One of the best experts on this subject based on the ideXlab platform.
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Efficient matrix-product state method for Periodic Boundary conditions
Physical Review B, 2010Co-Authors: Peter Pippan, Steven R. White, Hans Gerd EvertzAbstract:We introduce an efficient method to calculate the ground state of one-dimensional lattice models with Periodic Boundary conditions. The method works in the representation of Matrix Product States (MPS), related to the Density Matrix Renormalization Group (DMRG) method. It improves on a previous approach by Verstraete et al. We introduce a factorization procedure for long products of MPS matrices, which reduces the computational effort from m^5 to m^3, where m is the matrix dimension, and m ~ 100 - 1000 in typical cases. We test the method on the S=1/2 and S=1 Heisenberg chains. It is also applicable to non-translationally invariant cases. The new method makes ground state calculations with Periodic Boundary conditions about as efficient as traditional DMRG calculations for systems with open boundaries.
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efficient matrix product state method for Periodic Boundary conditions
Physical Review B, 2010Co-Authors: Peter Pippan, Steven R. White, Hans Gerd EvertzAbstract:We introduce an efficient method to calculate the ground state of one-dimensional lattice models with Periodic Boundary conditions. The method works in the representation of matrix product states (MPS), related to the density matrix renormalization group (DMRG) method. It improves on a previous approach by Verstraete et al. We introduce a factorization procedure for long products of MPS matrices, which reduces the computational effort from ${m}^{5}$ to ${m}^{3}$, where $m$ is the matrix dimension, and $m\ensuremath{\simeq}100--1000$ in typical cases. We test the method on the $S=\frac{1}{2}$ and $S=1$ Heisenberg chains. It is also applicable to nontranslationally invariant cases. The method makes ground-state calculations with Periodic Boundary conditions about as efficient as traditional DMRG calculations for systems with open boundaries.
