Laplace's equation and the Dirichlet-Neumann map: a new mode for Mikhlin's method

Mikhlin's method for solving Laplace's equation in domains exterior to a number of closed contours is discussed with particular emphasis on the Dirichlet-Neutnann map. In the literature there already exit tyro computational modes for Mikhlin's method. Here a new mode is presented. The new mode is at least as stable as the previous modes. Furthermore, its computational complexity in the number of closed contours is better. As a result. highly. accurate solutions in domains exterior to tens of thousands of closed contours can be obtained on a simple workstation

Noise measurements and rail traffic development

Public involvement in the planning process is a prerequisite for democratic outcomes. Environmental issues regarding impacts of sound tend to be limited to mere exercises in noise estimation and guideline values. Such information is difficult for the layman to understand, and such a lack of understanding produces shortcomings in the democratic process. In addition to decibel calculations interpretable by experts, the sonic environment also can be described in more accessible ways. This article reports on a concrete planning case, the widening of the railway through Åkarp in southern Sweden, where the usual calculations of equivalent noise and maximum noise are undergoing critical analysis. In order to complement the noise description, a new measurement has been devised, “high noise time,” which is equal to the total time per 24 hours in which trains pass through a place without stopping. The frequency and duration of the passing of trains may be a better measure of disturbance than the maximum noise peak per passage or the equivalent (average) noise level distributed over 24 hours. Film technology also has been developed as a method for recording the frequency and duration of train passage

On using a zero lower bound on the physical density in material distribution topology optimization

The current paper studies the possibility of allowing a zero lower bound on the physical density in material distribution based topology optimization. We limit our attention to the standard test problem of minimizing the compliance of a linearly elastic structure subject to a constant forcing. First order tensor product Finite Elements discretize the problem. An elementwise constant material indicator function defines the discretized, elementwise constant, physical density by using filtering and penalization. To alleviate the ill-conditioning of the stiffness matrix, due to the variation of the elementwise constant physical density, we precondition the system. We provide a specific spectral analysis for large matrix sizes for the one-dimensional problem with Dirichlet\u2013Neumann conditions in detail, even if most of the mathematical tools apply also in a d-dimensional setting, d 652. It is easy to find an elementwise constant material indicator function so that the resulting preconditioned system matrix is singular when allowing the vanishing physical densities. However, for a large class of material indicator functions, the corresponding preconditioned system matrix has a condition number of the same order as the system matrix for the case when the physical density is one in all elements. Finally, we critically report and illustrate results from numerical experiments: as a conclusion, it is indeed possible to solve large-scale topology optimization problems, allowing a vanishing physical density, without encountering ill-conditioned system matrices during the optimization