52,518 research outputs found
On the Computation of Power in Volume Integral Equation Formulations
We present simple and stable formulas for computing power (including
absorbed/radiated, scattered and extinction power) in current-based volume
integral equation formulations. The proposed formulas are given in terms of
vector-matrix-vector products of quantities found solely in the associated
linear system. In addition to their efficiency, the derived expressions can
guarantee the positivity of the computed power. We also discuss the application
of Poynting's theorem for the case of sources immersed in dissipative
materials. The formulas are validated against results obtained both with
analytical and numerical methods for scattering and radiation benchmark cases
A Study of Different Modeling Choices For Simulating Platelets Within the Immersed Boundary Method
The Immersed Boundary (IB) method is a widely-used numerical methodology for
the simulation of fluid-structure interaction problems. The IB method utilizes
an Eulerian discretization for the fluid equations of motion while maintaining
a Lagrangian representation of structural objects. Operators are defined for
transmitting information (forces and velocities) between these two
representations. Most IB simulations represent their structures with
piecewise-linear approximations and utilize Hookean spring models to
approximate structural forces. Our specific motivation is the modeling of
platelets in hemodynamic flows. In this paper, we study two alternative
representations - radial basis functions (RBFs) and Fourier-based
(trigonometric polynomials and spherical harmonics) representations - for the
modeling of platelets in two and three dimensions within the IB framework, and
compare our results with the traditional piecewise-linear approximation
methodology. For different representative shapes, we examine the geometric
modeling errors (position and normal vectors), force computation errors, and
computational cost and provide an engineering trade-off strategy for when and
why one might select to employ these different representations.Comment: 33 pages, 17 figures, Accepted (in press) by APNU
Geodesics in Heat
We introduce the heat method for computing the shortest geodesic distance to
a specified subset (e.g., point or curve) of a given domain. The heat method is
robust, efficient, and simple to implement since it is based on solving a pair
of standard linear elliptic problems. The method represents a significant
breakthrough in the practical computation of distance on a wide variety of
geometric domains, since the resulting linear systems can be prefactored once
and subsequently solved in near-linear time. In practice, distance can be
updated via the heat method an order of magnitude faster than with
state-of-the-art methods while maintaining a comparable level of accuracy. We
provide numerical evidence that the method converges to the exact geodesic
distance in the limit of refinement; we also explore smoothed approximations of
distance suitable for applications where more regularity is required
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