Search results for "Finite element method"

Finite-element design sensitivity analysis for non-linear potential problems

1990

Design sensitivity analysis is performed for the finite-element system arising from the discretization of non-linear potential problems using isoparametric Lagrangian elements. The calculated sensitivity formulae are given in a simple matrix form. Applications to the design of electromagnets and airfoils are given.

Post‐processing of Gauss–Seidel iterations

1999

Comparison between the shifted-Laplacian preconditioning and the controllability methods for computational acoustics

2010

Processes that can be modelled with numerical calculations of acoustic pressure fields include medical and industrial ultrasound, echo sounding, and environmental noise. We present two methods for making these calculations based on Helmholtz equation. The first method is based directly on the complex-valued Helmholtz equation and an algebraic multigrid approximation of the discretized shifted-Laplacian operator; i.e. the damped Helmholtz operator as a preconditioner. The second approach returns to a transient wave equation, and finds the time-periodic solution using a controllability technique. We concentrate on acoustic problems, but our methods can be used for other types of Helmholtz pro…

An algebraic multigrid based shifted-Laplacian preconditioner for the Helmholtz equation

2007

A preconditioner defined by an algebraic multigrid cycle for a damped Helmholtz operator is proposed for the Helmholtz equation. This approach is well suited for acoustic scattering problems in complicated computational domains and with varying material properties. The spectral properties of the preconditioned systems and the convergence of the GMRES method are studied with linear, quadratic, and cubic finite element discretizations. Numerical experiments are performed with two-dimensional problems describing acoustic scattering in a cross-section of a car cabin and in a layered medium. Asymptotically the number of iterations grows linearly with respect to the frequency while for lower freq…

A damping preconditioner for time-harmonic wave equations in fluid and elastic material

2009

A physical damping is considered as a preconditioning technique for acoustic and elastic wave scattering. The earlier preconditioners for the Helmholtz equation are generalized for elastic materials and three-dimensional domains. An algebraic multigrid method is used in approximating the inverse of damped operators. Several numerical experiments demonstrate the behavior of the method in complicated two-dimensional and three-dimensional domains. peerReviewed

Electrochemical pH Control at Gold Nanowires

2018

In this work, interdigitated arrays of nanowire electrodes are used with one array acting as the working electrode while the other is used to generate the required protons. Finite element simulations of the pH control electrodes were performed to provide insight on the generation and subsequent diffusion of protons. This informed the inter-tine spacing of the electrodes used.. This electrochemical pH control method was then used to enable the detection of analytes of interest.

Comparison of hemodynamic and structural indices of ascending thoracic aortic aneurysm as predicted by 2-way FSI, CFD rigid wall simulation and patie…

2018

Patient-specific computational modeling is increasingly being used to predict structural and hemodynamic parameters, especially when current clinical tools are not accessible. Indeed, pathophysiology of ascending thoracic aortic aneurysm (ATAA) has been simulated to quantify the risk of complications by novel prognostic parameters and thus to improve the clinical decision-making process related to the intervention of ATAAs. In this study, the relevance of aneurysmal wall elasticity in determining parameters of clinical importance, such as the wall shear stress (WSS), is discussed together with the significance of applying realistic boundary conditions to consider the aortic stretch and twis…

Closed form coefficients in the Symmetric Boundary Element Approach

2006

Abstract In the area of the structural analysis, the problems connected to the use of the symmetric Galerkin Boundary Element Method (SGBEM) must be investigated especially in the mathematical and computational difficulties that are present in computing the solving system coefficients. Indeed, any coefficient is made by double integrals including often fundamental solutions having a high degree of singularity. Therefore, the related computation proves to be difficult in the solution. This paper suggests a simple computation technique of the coefficients obtained in closed form. Using a particular matrix, called ‘progenitor’ matrix [Panzeca T, Cucco F, Terravecchia S. Symmetric boundary elem…

Nonlocal elasticity and related variational principles

2001

Abstract The Eringen model of nonlocal elasticity is considered and its implications in solid mechanics studied. The model is refined by assuming an attenuation function depending on the `geodetical distance' between material particles, such that in the diffusion processes of the nonlocality effects certain obstacles as holes or cracks existing in the domain can be circumvented. A suitable thermodynamic framework with nonlocality is also envisaged as a firm basis of the model. The nonlocal elasticity boundary-value problem for infinitesimal displacements and quasi-static loads is addressed and the conditions for the solution uniqueness are established. Three variational principles, nonlocal…

Internal fe approximation of spaces of divergence-free functions in three-dimensional domains

1986

SUMMARY The space of divergence-free vector functions with vanishing normal flux on the boundary is approximated by subspaces of finite elements having the same property. An easy way of generating basis functions in these subspaces is shown.