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Questions tagged [helmholtz-equation]

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-1
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0answers
50 views

DG discretisation for first order Helmholtz equation

I am trying to implement a DG scheme for a first order wave (Helmholtz) equation in Fenics. The problem is: find $(u,P)$ in $\Omega = [0,1] \times [0,1]$ unit square domain, such that $$ \frac{\...
0
votes
1answer
135 views

Proving solution existence and uniqueness of the Helmholtz equation with Robin boundary conditions with complex coefficients

I am trying to solve the Helmholtz equation with Robin boundary conditions with complex coefficients and the weak formulation $$ \iint_\limits\Omega\nabla p_0(x,y)\nabla\left(\overline{v(x,y)}\right)...
4
votes
1answer
694 views

Weak Formulation of Helmholtz equation with a complex coefficient and complex source term

I'm trying to solve $$\nabla^2u + ku = f\text{ in } \Omega,$$ $$u=0 \text{ on }\partial\Omega,$$ where $\Omega$ is a unit square and $k,f$ have real and imaginary components as $k=k_r+k_ij$ and $f(x,...
5
votes
1answer
223 views

What is a good way to solve the following linear system? (repeatedly)

Let $n,m\in \mathbb{N}$ be such that $m\ge n$. Let $M_1\in \mathbb{R}^{n\times n}$, $\{M_{2},M_{3} \} \subset \mathbb{R}^{m\times m}$ be symmetric positive definite and computationally cheap to ...
2
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0answers
389 views

Solving the Helmholtz equation numerically

I am trying to solve the Helmholtz equation in some complex unbounded 2D domain: $$\left( \frac{\partial^2 \psi}{\partial x^2} + \frac{\partial^2 \psi}{\partial y^2} + E \right) u(x, y) = 0$$ ...
8
votes
2answers
305 views

Periodic Green's functions in integral equation methods in different frequency regimes

I'm asking about the solution of the Helmholtz equation on a periodic domain with piecewise constant wavespeed in different frequency regimes. One possible approach is to solving this problem is to ...
2
votes
0answers
107 views

Eigenmode constraints on a complex wave field

I'm studying the usual wave equation: $$ \frac{\partial^2 \psi}{\partial x^2} - \frac{1}{c^2} \frac{\partial^2 \psi}{\partial t^2} = 0$$ with complex field $\psi$, on a n-dimensional cube region of ...
7
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0answers
301 views

Energy conservation in the solution of the Helmholtz equation

This might be a silly question, but I know very little about the theoretical properties finite elements, so here goes. Suppose you were to solve the Helmholtz equation (let's say in 2D) with a ...