10,521 research outputs found

    A Hybrid Boundary Element Method for Elliptic Problems with Singularities

    Full text link
    The singularities that arise in elliptic boundary value problems are treated locally by a singular function boundary integral method. This method extracts the leading singular coefficients from a series expansion that describes the local behavior of the singularity. The method is fitted into the framework of the widely used boundary element method (BEM), forming a hybrid technique, with the BEM computing the solution away from the singularity. Results of the hybrid technique are reported for the Motz problem and compared with the results of the standalone BEM and Galerkin/finite element method (GFEM). The comparison is made in terms of the total flux (i.e. the capacitance in the case of electrostatic problems) on the Dirichlet boundary adjacent to the singularity, which is essentially the integral of the normal derivative of the solution. The hybrid method manages to reduce the error in the computed capacitance by a factor of 10, with respect to the BEM and GFEM

    Power computation for the triboelectric nanogenerator

    Full text link
    We consider, from a mathematical perspective, the power generated by a contact-mode triboelectric nanogenerator, an energy harvesting device that has been well studied recently. We encapsulate the behaviour of the device in a differential equation, which although linear and of first order, has periodic coefficients, leading to some interesting mathematical problems. In studying these, we derive approximate forms for the mean power generated and the current waveforms, and describe a procedure for computing the Fourier coefficients for the current, enabling us to show how the power is distributed over the harmonics. Comparisons with accurate numerics validate our analysis

    Linear approach to the orbiting spacecraft thermal problem

    Get PDF
    We develop a linear method for solving the nonlinear differential equations of a lumped-parameter thermal model of a spacecraft moving in a closed orbit. Our method, based on perturbation theory, is compared with heuristic linearizations of the same equations. The essential feature of the linear approach is that it provides a decomposition in thermal modes, like the decomposition of mechanical vibrations in normal modes. The stationary periodic solution of the linear equations can be alternately expressed as an explicit integral or as a Fourier series. We apply our method to a minimal thermal model of a satellite with ten isothermal parts (nodes) and we compare the method with direct numerical integration of the nonlinear equations. We briefly study the computational complexity of our method for general thermal models of orbiting spacecraft and conclude that it is certainly useful for reduced models and conceptual design but it can also be more efficient than the direct integration of the equations for large models. The results of the Fourier series computations for the ten-node satellite model show that the periodic solution at the second perturbative order is sufficiently accurate.Comment: 20 pages, 11 figures, accepted in Journal of Thermophysics and Heat Transfe

    The Decoupled Potential Integral Equation for Time-Harmonic Electromagnetic Scattering

    Full text link
    We present a new formulation for the problem of electromagnetic scattering from perfect electric conductors. While our representation for the electric and magnetic fields is based on the standard vector and scalar potentials A,ϕ{\bf A},\phi in the Lorenz gauge, we establish boundary conditions on the potentials themselves, rather than on the field quantities. This permits the development of a well-conditioned second kind Fredholm integral equation which has no spurious resonances, avoids low frequency breakdown, and is insensitive to the genus of the scatterer. The equations for the vector and scalar potentials are decoupled. That is, the unknown scalar potential defining the scattered field, ϕSc\phi^{Sc}, is determined entirely by the incident scalar potential ϕIn\phi^{In}. Likewise, the unknown vector potential defining the scattered field, ASc{\bf A}^{Sc}, is determined entirely by the incident vector potential AIn{\bf A}^{In}. This decoupled formulation is valid not only in the static limit but for arbitrary ω0\omega\ge 0.Comment: 33 pages, 7 figure
    corecore