The vector electric-field Helmholtz equation, containing cross-polarization terms, is factored to produce both pseudo-differential and exponential operator forms of a three-dimensional, one-way, ...

The Dirac equation is fundamental to quantum field theory, which makes it possible, for example, to describe the creation and annihilation of photons in the context of quantum electrodynamics. Quantum ...

The one-dimensional Helmholtz equation for a medium with arbitrary inhomogeneities is solved by a uniformly valid iteration technique. Unlike the Born-Newman series approach, this technique does not ...

The Helmholtz equation and the classical centered scheme for the 1D and 2D cases are presented first. In next section, the new method for the 1D and 2D cases using different uniform stencils is ...

Numerical reconstruction of scattering poles for the Helmholtz equation in 2 dimensions for Dirichlet/Neumann/Impedance boundary conditions This code corresponds to the algorithm described in the ...

Finally, we outline a proposal to implement the QB2X method into the chunkie framework, a MATLAB integral equation toolbox that parameterizes curves into chunkers and evaluates layer potentials ...

But the equation doesn’t work in practice. A pipe’s fundamental tone always sounds lower than the pipe’s length suggests it should according to Helmholtz’s formula.

Dear Lu Lu, Thank you for such a great package. I really consider deepXDE as a future working tool for my research interests. Here is my specific problem: First I tried to train the network for a ...