This article reviews several fast algorithms for boundary integral equations. After a brief introduction of the boundary integral equations for the Laplace and Helmholtz equations, we discuss in order the fast multipole method and its kernel independent variant, the hierarchical matrix framework, the wavelet based method, the high frequency fast multipole method, and the recently proposed multi...

The kernel-independent fast multipole method (KIFMM) proposed in [1] is of almost linear complexity. In the original KIFMM the time-consuming M2L translations are accelerated by FFT. However, when more equivalent points are used to achieve higher accuracy, the efficiency of the FFT approach tends to be lower because more auxiliary volume grid points have to be added. In this paper, all the tran...

We present the concept of fiber-flux density for locally quantifying white matter (WM) fiber bundles. By combining scalar diffusivity measures (e.g., fractional anisotropy) with fiber-flux measurements, we define new local descriptors called Fiber-Flux Diffusion Density (FFDD) vectors. Applying each descriptor throughout fiber bundles allows alongtract coupling of a specific diffusion measure w...

An active-antenna array with 18 transmit elements and 18 receive elements is designed and fabricated. This T/R array can work at two different frequencies (19.5 GHz and 21.5 GHz) with multiple levels of isolation between the transmit and receive channels. A hybrid element-level vector finite element and adaptive multilevel fast multipole method (ELVFEM/AMLFMA) is applied to simulation the perfo...

We describe the iterative solution of dense linear systems arising from a surface integral equation of electromagnetic scattering. The complex symmetric version of QMR has been used as an iterative solver together with a sparse approximate inverse preconditioner. The preconditioner is computed using the topological information from the computational mesh. The matrix-vector products are computed...

Fast Marching Methods, FMM, have a wide range of applications, including path planning and navigation, but rarely feature in surveys of path planning techniques. For some applications, however, FMM are more suitable than other popular techniques, such as A*. This paper provides a brief outline of how FMM may be applied to path planning problems and notes the strengths and weaknesses of the meth...

Curves are often used as anatomical features to match surfaces that represent biological objects, such as the human brain. Automated and semi-automated methods for extracting these curves usually rely on local properties of the surfaces such as the mean surface curvature without considering the global appearance of the curves themselves. These methods may require additional human intervention, ...