Boundary element methods for the wave equation based on hierarchical matrices and adaptive cross approximation

Time-domain Boundary Element Methods (BEM) have been successfully used in acoustics, optics and elastodynamics to solve transient problems numerically. However, the storage requirements are immense, since the fully populated system matrices have to be computed for a large number of time steps or frequencies. In this article, we propose a new approximation scheme for the Convolution Quadrature Method powered BEM, which we apply to scattering problems governed by the wave equation. We use $${\mathscr {H}}^2$$ H 2 -matrix compression in the spatial domain and employ an adaptive cross approximation algorithm in the frequency domain. In this way, the storage and computational costs are reduced significantly, while the accuracy of the method is preserved.

NUMERICAL SIMULATION OF TRI-LAYERED MATERIALS UNDER CONTACT LOAD

Various biomedical components, such as dental crowns and hip prostheses, data processing devices, and other numerous mechanical components that transmit load through a mechanical contact, may benefit from a tri-layer design. The coating may be optimized for wear protection and corrosion prevention, whereas the intermediate layer provides increased adhesion between the outer layer and the substrate, and confines the crack propagation. The solution to the contact problem involving tri-layered materials can be pursued numerically with the finite element or the boundary element methods, but semi-analytical techniques benefitting from the efficiency of the fast Fourier transform (FFT) technique have also been successfully applied. At the heart of the FFT-assisted approach lie the frequency response functions (FRFs), which are analytical solutions for fundamental problems of elasticity such as the Boussinesq and Cerruti problems, but expressed in the frequency domain. Considering recent efforts and results in application of FFT to convolution calculations in contact problems, the displacement arising in a tri-layer configuration is computed in the frequency domain, and the contact problem is subsequently solved in the space domain using a state-of-the-art algorithm based on the conjugate gradient method. The method relies on the FRFs derived in the literature for tri-layered materials, and the efficiency and accuracy of computations in the frequency domain is assured by using the Discrete Convolution Fast Fourier Technique (DCFFT) with influence coefficients derived from the FRFs. The computer program reproduces well-known results for bi-layered materials. Numerical simulations are performed for various configurations in which the elastic properties of the layers, as well as the frictional coefficient, are varied. By using the newly advanced simulation technique, design recommendations may be advanced for the optimal configuration of tri-layered materials under contact load.

Evaluation of Methodology for Lightning Impulse Voltage Distribution over High-Voltage Windings of Inductive Voltage Transformers

Knowledge of lightning impulse (LI) voltage distribution over transformer windings during the design stage of the transformer is very important. Specific design differences in inductive voltage transformers make the transient analysis approach different to the approach to the power transformers. In this paper, a methodology for acquiring lightning impulse voltage distribution over high-voltage (HV) winding of inductive voltage transformers is presented and evaluated. Resistance, inductance, and capacitance matrices are calculated using the integral and boundary element methods (BEM) approach. Additionally, in order to improve the capacitance matrix solver, adaptive cross approximation (ACA) is applied. These parameters are then used to solve the equivalent circuit model in time domain. In order to evaluate the methodology, an experimental and numerical investigation of the layer discretisation, iron core influence, and accuracy of the proposed methodology is performed. The comparison of numerical results with measurements confirms the validity of the methodology.