Homogeneous Dirichlet

Homogeneous Dirichlet conditions force the wavefield to be zero at the specified boundary.

In the scalar acoustic case, this simply gives

ϕ=0,on Γ,{`\\phi = 0,\\quad\\text{on~}\\Gamma,`}

and in elastic media, we obtain

u=0,on Γ.{`u = 0,\\quad\\text{on~}\\Gamma.`}

It is possible to fix only certain components of the displacement field u{`u`} in the elastic case.

Practical Advice

For coupled simulations of waves propagating along a fluid-solid interface, the homogeneous Dirichlet condition is the physically correct condition to describe the "free-surface condition" in water.

Further reading

More information on the practical use of absorbing boundaries can be found on the following pages: