Browsing by Author "Valtchev, Svilen S."
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- An instantaneous regulation for the wired and wireless super-resonant convertersPublication . Valtchev, Stanimir; Medeiros, Rui; Valtchev, Svilen S.; Klaassens, BenThe 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.
- Asymptotic Analysis of the Method of Fundamental Solutions for Acoustic Wave PropagationPublication . Valtchev, Svilen S.The asymptotic behavior of the Method of Fundamental Solutions (MFS) is analyzed, for the numerical solution of acoustic wave propagation problems in 2D and 3D bounded domains. As a consequence, a meshfree method, based on superposition of plane acoustic waves, referred to as the Plane Waves Method (PWM), is developed. Numerical examples are included in order to illustrate the relation between the two methods and the accuracy of the PWM.
- A meshfree method with plane waves for elastic wave propagation problemsPublication . Valtchev, Svilen S.In this paper, we address the meshfree numerical solution of time-harmonic linear elastic wave propagation problems in homogeneous media. In particular, we analyze the asymptotic behavior of the method of fundamental solutions (MFS) with source points located far away from the domain of interest. The asymptotic MFS is shown to be equivalent to a Trefftz method, here referred to as the plane waves method (PWM), based on superposition of shear and compressional elastic plane waves with different directions of propagation. Several numerical examples are included in order to illustrate the equivalence between the asymptotic MFS and the PWM. The convergence and stability of the PWM are also analyzed in smooth settings.
- A meshfree numerical method for acoustic wave propagation problems in planar domains with corners and cracksPublication . Antunes, Pedro R. S.; Valtchev, Svilen S.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.
- Solving boundary value problems on manifolds with a plane waves methodPublication . Alves, Carlos J. S.; Antunes, Pedro R. S.; Martins, Nuno F. M.; Valtchev, Svilen S.In this paper we consider a plane waves method as a numerical technique for solving boundary value problems for linear partial differential equations on manifolds. In particular, the method is applied to the Helmholtz–Beltrami equations. We prove density results that justify the completeness of the plane waves space and justify the approximation of domain and boundary data. A-posteriori error estimates and numerical experiments show that this simple technique may be used to accurately solve boundary value problems on manifolds.
- Trefftz methods with cracklets and their relation to BEM and MFSPublication . Alves, Carlos J.S.; Martins, Nuno F.M.; Valtchev, Svilen S.In this paper we consider Trefftz methods which are based on functions defined by single layer or double layer potentials, integrals of the fundamental solution, or their normal derivative, on cracks. These functions are called cracklets, and satisfy the partial differential equation, as long as the crack support is not placed inside the domain. A boundary element method (BEM) interpretation is to consider these cracks as elements of the original boundary, in a direct BEM approach, or elements of an artificial boundary, in an indirect BEM approach. In this paper we consider the cracklets just as basis functions in Trefftz methods, as the method of fundamental solutions (MFS). We focus on the 2D Laplace equation, and establish some comparisons and connections between these methods with cracklets and standard approaches like the BEM, indirect BEM, and the MFS. Namely, we propose the enrichment of the MFS basis with the cracklets. Several numerical simulations are presented to test the performance of the methods, in particular comparing the results with the MFS and the BEM.