2,175 research outputs found
Development of an Optimization-Based Atomistic-to-Continuum Coupling Method
Atomistic-to-Continuum (AtC) coupling methods are a novel means of computing
the properties of a discrete crystal structure, such as those containing
defects, that combine the accuracy of an atomistic (fully discrete) model with
the efficiency of a continuum model. In this note we extend the
optimization-based AtC, formulated in arXiv:1304.4976 for linear,
one-dimensional problems to multi-dimensional settings and arbitrary
interatomic potentials. We conjecture optimal error estimates for the
multidimensional AtC, outline an implementation procedure, and provide
numerical results to corroborate the conjecture for a 1D Lennard-Jones system
with next-nearest neighbor interactions.Comment: 12 pages, 3 figure
Electronic structure of wet DNA.
The electronic properties of a Z-DNA crystal synthesized in the laboratory are investigated by means of density-functional theory Car-Parrinello calculations. The electronic structure has a gap of only 1.28 eV. This separates a manifold of 12 occupied states which came from the pi guanine orbitals from the lowest empty states in which the electron is transferred to the Na+ from PO-4 groups and water molecules. We have evaluated the anisotropic optical conductivity. At low frequency the conductivity is dominated by the pi-->Na+ transitions. Our calculation demonstrates that the cost of introducing electron holes in wet DNA strands could be lower than previously anticipated
Optimal control in heterogeneous domain decomposition methods
Some new domain decomposition methods (DDM) based on optimal control approach are introduced for the coupling of first- and second-order equations on overlapping subdomains. Several cost functionals and control functions are proposed. Uniqueness and existence results are proved for the coupled problem and the convergence of iterative processes is analyze
The INTERNODES method for applications in contact mechanics and dedicated preconditioning techniques
The mortar finite element method is a well-established method for the numerical solution of partial differential equations on domains displaying non-conforming interfaces. The method is known for its application in computational contact mechanics. However, its implementation remains challenging as it relies on geometrical projections and unconventional quadrature rules. The INTERNODES (INTERpolation for NOn-conforming DEcompositionS) method, instead, could overcome the implementation difficulties thanks to flexible interpolation techniques. Moreover, it was shown to be at least as accurate as the mortar method making it a very promising alternative for solving problems in contact mechanics. Unfortunately, in such situations the method requires solving a sequence of ill-conditioned linear systems. In this paper, preconditioning techniques are designed and implemented for the efficient solution of those linear systems
A matrix–free high–order solver for the numerical solution of cardiac electrophysiology
We propose a matrix-free solver for the numerical solution of the cardiac electrophysiology model consisting of the monodomain nonlinear reaction-diffusion equation coupled with a system of ordinary differential equations for the ionic species. Our numerical approximation is based on the high-order Spectral Element Method (SEM) to achieve accurate numerical discretization while employing a much smaller number of Degrees of Freedom than first-order Finite Elements. We combine vectorization with sum- factorization, thus allowing for a very efficient use of high-order polynomials in a high performance computing framework. We validate the effectiveness of our matrix-free solver in a variety of applications and perform different electrophysiological simulations ranging from a simple slab of cardiac tissue to a realistic four-chamber heart geometry. We compare SEM to SEM with Numerical Integration (SEM-NI), showing that they provide comparable results in terms of accuracy and efficiency. In both cases, increasing the local polynomial degree p leads to better numerical results and smaller computational times than reducing the mesh size h. We also implement a matrix-free Geometric Multigrid preconditioner that results in a comparable number of linear solver iterations with respect to a state-of-the-art matrix-based Algebraic Multigrid preconditioner. As a matter of fact, the matrix-free solver proposed here yields up to 45x speed-up with respect to a conventional matrix-based solver. (c) 2023 Elsevier Inc. All rights reserved
Does the quantity of enteral nutrition affect outcomes in critically ill trauma patients?
Abstract from Clinical Nutrition Week, Orlando, FL, January 29-February 2, 2005
FE modelling strategies of weld repair in pre-stressed thin components
Two computational procedures have been developed in the commercial finite element (FE) software codes Sysweld and Abaqus to analyse and predict the residual stress state after the repair of small weld defects in thin structural components. The numerical models allow the effects of the repair to be studied when a pre-existing residual stress field is present in the fabricated part and cannot be relieved by a thermal treatment.
In this work the modelling strategies are presented and tested by simulating a repair of longitudinal welds in thin sheets of Inconel 718 (IN718). Although the numerical strategies in the two codes are intrinsically different, the results show a significant agreement, predicting a notable effect imposed by the initial residual stress
A multidomain spectral method for solving elliptic equations
We present a new solver for coupled nonlinear elliptic partial differential
equations (PDEs). The solver is based on pseudo-spectral collocation with
domain decomposition and can handle one- to three-dimensional problems. It has
three distinct features. First, the combined problem of solving the PDE,
satisfying the boundary conditions, and matching between different subdomains
is cast into one set of equations readily accessible to standard linear and
nonlinear solvers. Second, touching as well as overlapping subdomains are
supported; both rectangular blocks with Chebyshev basis functions as well as
spherical shells with an expansion in spherical harmonics are implemented.
Third, the code is very flexible: The domain decomposition as well as the
distribution of collocation points in each domain can be chosen at run time,
and the solver is easily adaptable to new PDEs. The code has been used to solve
the equations of the initial value problem of general relativity and should be
useful in many other problems. We compare the new method to finite difference
codes and find it superior in both runtime and accuracy, at least for the
smooth problems considered here.Comment: 31 pages, 8 figure
Complex microwave conductivity of Na-DNA powders
We report the complex microwave conductivity, , of
Na-DNA powders, which was measured from 80 K to 300 K by using a microwave
cavity perturbation technique. We found that the magnitude of near
room temperature was much larger than the contribution of the surrounding water
molecules, and that the decrease of with decreasing temperature was
sufficiently stronger than that of the conduction of counterions. These results
clearly suggest that the electrical conduction of Na-DNA is intrinsically
semiconductive.Comment: 16 pages, 7 figure
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