10,521 research outputs found
A Hybrid Boundary Element Method for Elliptic Problems with Singularities
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
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
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
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The Decoupled Potential Integral Equation for Time-Harmonic Electromagnetic Scattering
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 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, , is determined entirely by the incident scalar
potential . Likewise, the unknown vector potential defining the
scattered field, , is determined entirely by the incident vector
potential . This decoupled formulation is valid not only in the
static limit but for arbitrary .Comment: 33 pages, 7 figure
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