The Experts below are selected from a list of 28704 Experts worldwide ranked by ideXlab platform
Yongjie Jessica Zhang - One of the best experts on this subject based on the ideXlab platform.
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the divergence conforming immersed boundary method application to vesicle and capsule dynamics
Journal of Computational Physics, 2021Co-Authors: Hugo Casquero, Carles Bonacasas, Deepesh Toshniwal, Thomas J R Hughes, H Gomez, Yongjie Jessica ZhangAbstract:Abstract We extend the recently introduced divergence-conforming immersed boundary (DCIB) method [1] to fluid-structure interaction (FSI) problems involving closed co-dimension one solids. We focus on capsules and vesicles, whose discretization is particularly challenging due to the higher-order derivatives that appear in their formulations. In two-dimensional settings, we employ cubic B-splines with periodic knot vectors to obtain Discretizations of closed curves with C 2 inter-element continuity. In three-dimensional settings, we use analysis-suitable bi-cubic T-splines to obtain Discretizations of closed surfaces with at least C 1 inter-element continuity. Large spurious changes of the fluid volume inside closed co-dimension one solids are a well-known issue for IB methods. The DCIB method results in volume changes orders of magnitude lower than conventional IB methods. This is a byproduct of discretizing the velocity-pressure pair with divergence-conforming B-splines, which lead to negligible incompressibility errors at the Eulerian level. The higher inter-element continuity of divergence-conforming B-splines is also crucial to avoid the quadrature/interpolation errors of IB methods becoming the dominant discretization error. Benchmark and application problems of vesicle and capsule dynamics are solved, including mesh-independence studies and comparisons with other numerical methods.
Vikram Gavini - One of the best experts on this subject based on the ideXlab platform.
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higher order adaptive finite element methods for kohn sham density functional theory
Journal of Computational Physics, 2013Co-Authors: Phani Motamarri, M R Nowak, Kenneth W Leiter, Jaroslaw Knap, Vikram GaviniAbstract:We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn-Sham density-functional theory (DFT). To this end, we develop an a priori mesh-adaption technique to construct a close to optimal finite-element discretization of the problem. We further propose an efficient solution strategy for solving the discrete eigenvalue problem by using spectral finite-elements in conjunction with Gauss-Lobatto quadrature, and a Chebyshev acceleration technique for computing the occupied eigenspace. The proposed approach has been observed to provide a staggering 100-200-fold computational advantage over the solution of a generalized eigenvalue problem. Using the proposed solution procedure, we investigate the computational efficiency afforded by higher-order finite-element Discretizations of the Kohn-Sham DFT problem. Our studies suggest that staggering computational savings-of the order of 1000-fold-relative to linear finite-elements can be realized, for both all-electron and local pseudopotential calculations, by using higher-order finite-element Discretizations. On all the benchmark systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemical accuracy, suggesting that the hexic spectral-element may be an optimal choice for the finite-element discretization of the Kohn-Sham DFT problem. A comparative study of the computational efficiency of the proposed higher-order finite-element Discretizations suggests that the performance of finite-element basis is competing with the plane-wave discretization for non-periodic local pseudopotential calculations, and compares to the Gaussian basis for all-electron calculations to within an order of magnitude. Further, we demonstrate the capability of the proposed approach to compute the electronic structure of a metallic system containing 1688 atoms using modest computational resources, and good scalability of the present implementation up to 192 processors.
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higher order adaptive finite element methods for orbital free density functional theory
Journal of Computational Physics, 2012Co-Authors: Phani Motamarri, Jaroslaw Knap, Mrinal Iyer, Vikram GaviniAbstract:In the present work, we study various numerical aspects of higher-order finite-element Discretizations of the non-linear saddle-point formulation of orbital-free density-functional theory. We first investigate the robustness of viable solution schemes by analyzing the solvability conditions of the discrete problem. We find that a staggered solution procedure where the potential fields are computed consistently for every trial electron-density is a robust solution procedure for higher-order finite-element Discretizations. We next study the convergence properties of higher-order finite-element Discretizations of orbital-free density functional theory by considering benchmark problems that include calculations involving both pseudopotential as well as Coulomb singular potential fields. Our numerical studies suggest close to optimal rates of convergence on all benchmark problems for various orders of finite-element approximations considered in the present study. We finally investigate the computational efficiency afforded by various higher-order finite-element Discretizations, which constitutes the main aspect of the present work, by measuring the CPU time for the solution of discrete equations on benchmark problems that include large Aluminum clusters. In these studies, we use mesh coarse-graining rates that are derived from error estimates and an a priori knowledge of the asymptotic solution of the far-field electronic fields. Our studies reveal a significant 100-1000 fold computational savings afforded by the use of higher-order finite-element discretization, alongside providing the desired chemical accuracy. We consider this study as a step towards developing a robust and computationally efficient discretization of electronic structure calculations using the finite-element basis.
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a numerical analysis of the finite element discretization of orbital free density functional theory
2011Co-Authors: Phani Motamarri, Jaroslaw Knap, Mrinal Iyer, Vikram GaviniAbstract:In the present work, we investigate the computational efficiency afforded by higherorder finite-element discretization of the saddle-point formulation of orbital-free densityfunctional theory. We first investigate the robustness of viable solution schemes by analyzing the solvability conditions of the discrete problem. We find that a staggered solution procedure where the potential fields are computed consistently for every trial electrondensity is a robust solution procedure for higher-order finite-element Discretizations. We next study the numerical convergence rate for various orders of finite-element approximations on benchmark problems. We obtain close to optimal convergence rates in our studies, although orbital-free density-functional theory is nonlinear in nature and some benchmark problems have Coulomb singular potential fields. We finally investigate the computational efficiency of various higher-order finite-element Discretizations by measuring the CPU time for the solution of discrete equations on benchmark problems that include large Aluminum clusters. In these studies, we use optimal mesh coarse-graining rates that are derived from error estimates and a priori knowledge of the asymptotic solution of electronic fields. Our studies reveal a significant 100-1000 fold computational savings afforded by the use of higher-order finite-element discretization, alongside providing the desired chemical accuracy. We consider this study as a step towards developing a robust and computationally efficient discretization of electronic structure calculations using the finite-element basis.
Hugo Casquero - One of the best experts on this subject based on the ideXlab platform.
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the divergence conforming immersed boundary method application to vesicle and capsule dynamics
Journal of Computational Physics, 2021Co-Authors: Hugo Casquero, Carles Bonacasas, Deepesh Toshniwal, Thomas J R Hughes, H Gomez, Yongjie Jessica ZhangAbstract:Abstract We extend the recently introduced divergence-conforming immersed boundary (DCIB) method [1] to fluid-structure interaction (FSI) problems involving closed co-dimension one solids. We focus on capsules and vesicles, whose discretization is particularly challenging due to the higher-order derivatives that appear in their formulations. In two-dimensional settings, we employ cubic B-splines with periodic knot vectors to obtain Discretizations of closed curves with C 2 inter-element continuity. In three-dimensional settings, we use analysis-suitable bi-cubic T-splines to obtain Discretizations of closed surfaces with at least C 1 inter-element continuity. Large spurious changes of the fluid volume inside closed co-dimension one solids are a well-known issue for IB methods. The DCIB method results in volume changes orders of magnitude lower than conventional IB methods. This is a byproduct of discretizing the velocity-pressure pair with divergence-conforming B-splines, which lead to negligible incompressibility errors at the Eulerian level. The higher inter-element continuity of divergence-conforming B-splines is also crucial to avoid the quadrature/interpolation errors of IB methods becoming the dominant discretization error. Benchmark and application problems of vesicle and capsule dynamics are solved, including mesh-independence studies and comparisons with other numerical methods.
Thomas J R Hughes - One of the best experts on this subject based on the ideXlab platform.
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the divergence conforming immersed boundary method application to vesicle and capsule dynamics
Journal of Computational Physics, 2021Co-Authors: Hugo Casquero, Carles Bonacasas, Deepesh Toshniwal, Thomas J R Hughes, H Gomez, Yongjie Jessica ZhangAbstract:Abstract We extend the recently introduced divergence-conforming immersed boundary (DCIB) method [1] to fluid-structure interaction (FSI) problems involving closed co-dimension one solids. We focus on capsules and vesicles, whose discretization is particularly challenging due to the higher-order derivatives that appear in their formulations. In two-dimensional settings, we employ cubic B-splines with periodic knot vectors to obtain Discretizations of closed curves with C 2 inter-element continuity. In three-dimensional settings, we use analysis-suitable bi-cubic T-splines to obtain Discretizations of closed surfaces with at least C 1 inter-element continuity. Large spurious changes of the fluid volume inside closed co-dimension one solids are a well-known issue for IB methods. The DCIB method results in volume changes orders of magnitude lower than conventional IB methods. This is a byproduct of discretizing the velocity-pressure pair with divergence-conforming B-splines, which lead to negligible incompressibility errors at the Eulerian level. The higher inter-element continuity of divergence-conforming B-splines is also crucial to avoid the quadrature/interpolation errors of IB methods becoming the dominant discretization error. Benchmark and application problems of vesicle and capsule dynamics are solved, including mesh-independence studies and comparisons with other numerical methods.
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three dimensional mortar based frictional contact treatment in isogeometric analysis with nurbs
Computer Methods in Applied Mechanics and Engineering, 2012Co-Authors: I Temizer, P. Wriggers, Thomas J R HughesAbstract:A three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS is presented in the finite deformation regime. Within a setting where the NURBS discretization of the contact surface is inherited directly from the NURBS discretization of the volume, the contact integrals are evaluated through a mortar approach where the geometrical and frictional contact constraints are treated through a projection to control point quantities. The formulation delivers a non-negative pressure distribution and minimally oscillatory local contact interactions with respect to alternative Lagrange Discretizations independent of the discretization order. These enable the achievement of improved smoothness in global contact forces and moments through higher-order geometrical descriptions. It is concluded that the presented mortar-based approach serves as a common basis for treating isogeometric contact problems with varying orders of discretization throughout the contact surface and the volume.
Ludmil T Zikatanov - One of the best experts on this subject based on the ideXlab platform.
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stability and monotonicity for some Discretizations of the biot s consolidation model
Computer Methods in Applied Mechanics and Engineering, 2016Co-Authors: Carmen Rodrigo, F J Gaspar, Ludmil T ZikatanovAbstract:Abstract We consider finite element Discretizations of the Biot’s consolidation model in poroelasticity with MINI and stabilized P1–P1 elements. We analyze the convergence of the fully discrete model based on spatial discretization with these types of finite elements and implicit Euler method in time. We also address the issue related to the presence of non-physical oscillations in the pressure approximation for low permeabilities and/or small time steps. We show that even in 1D a Stokes-stable finite element pair fails to provide a monotone discretization for the pressure in such regimes. We then introduce a stabilization term which removes the oscillations. We present numerical results confirming the monotone behavior of the stabilized schemes.
