Search results for "finite element method"
showing 10 items of 746 documents
Finite element approximation for a div-rot system with mixed boundary conditions in non-smooth plane domains
1984
The authors examine a finite element method for the numerical approximation of the solution to a div-rot system with mixed boundary conditions in bounded plane domains with piecewise smooth boundary. The solvability of the system both in an infinite and finite dimensional formulation is proved. Piecewise linear element fields with pointwise boundary conditions are used and their approximation properties are studied. Numerical examples indicating the accuracy of the method are given. peerReviewed
Inverse problems and invisibility cloaking for FEM models and resistor networks
2013
In this paper we consider inverse problems for resistor networks and for models obtained via the finite element method (FEM) for the conductivity equation. These correspond to discrete versions of the inverse conductivity problem of Calderón. We characterize FEM models corresponding to a given triangulation of the domain that are equivalent to certain resistor networks, and apply the results to study nonuniqueness of the discrete inverse problem. It turns out that the degree of nonuniqueness for the discrete problem is larger than the one for the partial differential equation. We also study invisibility cloaking for FEM models, and show how an arbitrary body can be surrounded with a layer …
An optimal local active noise control method based on stochastic finite element models
2013
A new method is presented to obtain a local active noise control that is optimal in stochastic environment. The method uses numerical acoustical modeling that is performed in the frequency domain by using a sequence of finite element discretizations of the Helmholtz equation. The stochasticity of domain geometry and primary noise source is considered. Reference signals from an array of microphones are mapped to secondary loudspeakers, by an off-line optimized linear mapping. The frequency dependent linear mapping is optimized to minimize the expected value of error in a quiet zone, which is approximated by the numerical model and can be interpreted as a stochastic virtual microphone. A leas…
On FE-grid relocation in solving unilateral boundary value problems by FEM
1992
We consider FE-grid optimization in elliptic unilateral boundary value problems. The criterion used in grid optimization is the total potential energy of the system. It is shown that minimization of this cost functional means a decrease of the discretization error or a better approximation of the unilateral boundary conditions, Design sensitivity analysis is given with respect to the movement of nodal points. Numerical results for the Dirichlet-Signorini problem for the Laplace equation and the plane elasticity problem with unilateral boundary conditions are given. In plane elasticity we consider problems with and without friction. peerReviewed
A fast Fourier transform based direct solver for the Helmholtz problem
2018
This article is devoted to the efficient numerical solution of the Helmholtz equation in a two‐ or three‐dimensional (2D or 3D) rectangular domain with an absorbing boundary condition (ABC). The Helmholtz problem is discretized by standard bilinear and trilinear finite elements on an orthogonal mesh yielding a separable system of linear equations. The main key to high performance is to employ the fast Fourier transform (FFT) within a fast direct solver to solve the large separable systems. The computational complexity of the proposed FFT‐based direct solver is O(N log N) operations. Numerical results for both 2D and 3D problems are presented confirming the efficiency of the method discussed…
Some Considerations on 3-D and 2-D Numerical Models for the Assessment of the Stability of Underground Caves
2014
The application of numerical modeling to the analysis of the stability of both natural and man-made underground caves is rapidly increasing due to the availability of powerful numerical codes, that can account for either continuum or discontinuum behavior of the rock masses. Numerical methods allow to overcome traditional methods for cave stability analysis that assume too simplified geometrical, geological and geomechanical conditions. Further, they are also able to assess the potential failure mechanisms of underground systems. On the other hand, the application of numerical methods requires availability of a detailed geo-structural survey of the cave, as well as a proper geomechanical ch…
Guided Wave Techniques for Damage Detection in Composite Aerospace Structures
2018
Composite materials make up an increasing portion of today’s aerospace structures (see, e.g. Boeing 787 and Airbus 380). These aircrafts’ fuselage, for example, is composed of a laminated composite skin connected to composite stringers and C-frames. Of primary importance is the detection of damage in these built-up structures, whether caused by the manufacturing process or in service (e.g. impacts). A related issue is the characterization of the composite (visco)elastic mechanical properties, that can also be related to the quantification of potential damage. Guided elastic waves propagating in the ~100s kHz regime lend themselves to provide the necessary sensitivity to these two conditions…
Mathematical modelling of sustainable bioresidual concrete
2019
In the production of cement, which is the main component of concrete production, the process generates about 5% of the global carbon dioxide emissions. In addition, bioproduct and pulp mills produce signi_cant quantities of soda ash and bio-ash, which is still largely unused. In this paper we will introduce our study related to improving the environmental friendliness of concrete used in construction by utilizing pulp mill waste while its long-term durability and strength and porosity properties meet the goals set for construction. The project `sustainable bioresidual concrete' is on-going and only preliminary numerical results with measurements are presented here. peerReviewed
Optimal Heating of an Indoor Swimming Pool
2020
This work presents the derivation of a model for the heating process of the air of a glass dome, where an indoor swimming pool is located in the bottom of the dome. The problem can be reduced from a three dimensional to a two dimensional one. The main goal is the formulation of a proper optimization problem for computing the optimal heating of the air after a given time. For that, the model of the heating process as a partial differential equation is formulated as well as the optimization problem subject to the time-dependent partial differential equation. This yields the optimal heating of the air under the glass dome such that the desired temperature distribution is attained after a given…
On the Fast and Rigorous Analysis of Compensated Waveguide Junctions Using Off-Centered Partial-Height Metallic Posts
2007
In this paper, we present an efficient and rigorous method, based on the 3-D boundary integral-resonant-mode expansion technique, for the analysis of multiport rectangular waveguide junctions compensated with partial-height cylindrical metallic posts. The electrical performance of a great variety of commonly used wideband microwave circuits has been improved drastically thanks to the introduction of a new design parameter, i.e., the relative position of the metallic post in the structure. To the authors' knowledge, this parameter has not been taken into account in previous studies concerning compensated junctions using partial-height metallic posts. The developed tool has been successfully …