Svilen S. Valtchev

A meshfree numerical method for acoustic wave propagation problems in planar domains with corners and cracks

The numerical solution of acoustic wave propagation problems in planar domains with corners and cracks is considered. Since the exact solution of such problems is singular in the neighborhood of the geometric singularities the standard meshfree methods, based on global interpolation by analytic functions, show low accuracy. In order to circumvent this issue, a meshfree modification of the method of fundamental solutions is developed, where the approximation basis is enriched by an extra span of corner adapted non-smooth shape functions. The high accuracy of the new method is illustrated by solving several boundary value problems for the Helmholtz equation, modelling physical phenomena from the fields of room acoustics and acoustic resonance.

A Kansa Type Method Using Fundamental Solutions Applied to Elliptic PDEs

A Kansa type modification of the Method of Fundamental Solutions (MFS) is presented. This allows us to apply the MFS to a larger class of elliptic problems. In the case of inhomogeneous problems we reduce to a single linear system, contrary to previous methods where two linear systems are solved, one for the particular solution and one for the homogeneous solution of the problem. Here the solution is approximated using fundamental solutions of the Helmholtz equation. Several numerical tests in 2D will be presented in order to illustrate the convergence of the method. Mixed, Dirichlet-Neumann, boundary conditions will be considered.

Improved strategy for an instantaneous super-resonant converter regulation

The proposed regulation strategy consists in obtaining at the right time the correct information about the energy contained in the resonant tank. This information allows a stable operation of the switches and a higher efficiency of any Series Loaded Series Resonant (SLSR) power converter, especially when contactless energy transfer is concerned. The strategy is based on guaranteeing the correct portion of energy transported by the resonant tank to the load. The portion has to vary corresponding to the error signal taken from the output voltage and remains unchanged if the error signal is at its minimum. In a certain way this method is similar to the Current Mode Control of the classical power converters. The viability of the idea is demonstrated by simulation of a realistic analogue circuit (on preparation for a digital implementation in the near future).

The Efficient and Stable Charging of Electric Vehicle Batteries: Simplified Instantaneous Regulation

The future charging of the growing fleet of Electric Vehicles (EV) requires new solutions that guarantee a better efficiency and widely spread chargers. Both in fast charging and in slow charging of the electric vehicle (EV) and hybrid electric vehicle (HEV), the wireless charger is the better choice. The wired charger is limited by its cabling and relatively lower output voltage, while the contactless charger can be more universal and safe. What rests to be discovered is the more efficient energy transfer that would have a stable operation. The strategy is based on guaranteeing the correct portion of energy transported by the resonant tank to the load. Some results are shown from this implementation of the instantaneous energy control.

An instantaneous regulation for the wired and wireless super-resonant converters

The paper develops further the method presented in [12], [14], based on energy balance in the resonant tank. This method allows a stable operation of the switches and a higher efficiency of any Series Loaded Series Resonant (SLSR) power converter, especially when contactless energy transfer is concerned. The strategy is based on guaranteeing the correct portion of energy transported by the resonant tank to the load. The portion has to vary corresponding to the error signal taken from the output voltage and remains unchanged if the error signal from the output is at its minimum. In a certain way this method is similar to the Current Mode Control of the classical power converters.

Comparison between Meshfree and Boundary Element methods applied to BVPs in domains with corners

A Dirichlet boundary value problem (BVP) for the Laplace equation will be considered in a bounded domain with corners. Two distinct types of numerical methods will be applied for the solution of this problem. A modification of the Boundary Element Method (BEM), as presented in [1], based on the double-layer potencial representation of the solution will be applied. Both piecewise constant and piecewise linear spline collocation will be used for the approximate solution of the resulting Fredholm integral equation of the second kind. Quadratic order of convergence is achieved in this case. On the other hand, the classical Method of Fundamental Solutions (MFS, e.g. [2]) will be applied. It is claimed that this meshfree method exhibits exponential rate of convergence when regular data (and domain) is considered, e.g. [3], [4]. Numerical results for polygonal domains will be presented. The importance of the location of the artificial boundary and the choice of the source points will be discussed for the MFS. The numerical methods will be compared in terms of absolute error of the approximate solution for a fixed number of boundary knots/boundary elements.