A sharp relative-error bound for the Helmholtz h-FEM at high frequency

Sharp High-Frequency Estimates for the Helmholtz Equation and Applications to Boundary Integral Equations

We consider three problems for the Helmholtz equation in interior and exterior domains in R, (d = 2, 3): the exterior Dirichlet-to-Neumann and Neumann-to-Dirichlet problems for outgoing solutions, and the interior impedance problem. We derive sharp estimates for solutions to these problems that, in combination, give bounds on the inverses of the combined-field boundary integral operators for ex...

Sharp ULP rounding error bound for the hypotenuse function

The hypotenuse function, z = √ x2 + y2, is sometimes included in math library packages. Assuming that it is being computed by a straightforward algorithm, in a binary floating point environment, with round to nearest rounding mode, a sharp roundoff error bound is derived, for arbitrary precision. For IEEE single precision, or higher, the bound implies that |z − z| < 1.222 ulp(z) and |z − z| < 1...

A Helmholtz coil for high frequency high field intensity applications

In this work a general introduction to Helmholtz coil is presented and then attention is on a practical implementation of a wideband (50 kHz) coil for high magnetic flux density applications (several mT may be obtained). Field uniformity is within ±1.5% and ±0.35% inside cubic volumes of 25% and 10% of the coil side respectively, so suitable also for high accuracy applications such as sensor ca...

Feti-h: a Scalable Domain Decomposition Method for High Frequency Exterior Helmholtz Problems

Approximation of the high-frequency Helmholtz kernel by nested directional interpolation: error analysis