For small deformations the equilibrium equation in the displacement formulation is 
(μ + λ)∇divu + μΔu
+ f = 0, f = div(I Ta) = ∇Ta,
where u = (X, Y) is displacement of a point from equilibrium position,
Ta represents the active stress in cardiac tissue , μ, λ are Lame parameters
(we put μ = 1 ). Using 2-nd order finite differences we obtain the approximate equation
(2 + λ)(Xi+1,j + Xi-1,j - 2Xi,j ) +
Xi,j+1 + Xi,j-1 - 2Xi,j + (Yi+1,j+1 + Yi-1,j-1
- Yi+1,j-1 - Yi-1,j+1 )(1 + λ)/4 + h2Fxi,j = 0,
Fxi,j = (Tai+1,j - Tai-1,j )/2h. (*)
2D weighted Jacobi relaxation algorithm on CPU
For weighted Jacobi relaxation  of (Xi,j , Yi,j ) on
n×n grid we rewrite equations (*) as
2(3 + λ)Xi,j = (2 + λ)(Xi+1,j + Xi-1,j ) +
Xi,j+1 + Xi,j-1 + (Yi+1,j+1 + Yi-1,j-1
- Yi+1,j-1 - Yi-1,j+1 )(1 + λ)/4 + h2Fxi,j where Ta ~ exp[-(r/a)2]. 50 cross-sections Xi, n/2 and
error log max |Xi,jnew - Xi,jold|
(the red curve below) are ploted after every 2it iterations.
Set it = 50 to get accurate displacement values.
You can check that relaxation is fast for small n (e.g. n = 32)
but it is very slow for fine-grids.
 Linear elasticity (Wiki)
 M.P. Nasha, A.V. Panfilov
Electromechanical model of excitable tissue to study reentrant cardiac arrhythmias Progress in Biophysics & Molecular Biology 85 (2004) 501.
 William L. Briggs, Van Emden Henson, Steve F. McCormick
A Multigrid Tutorial
(look at "Tutorial Slides")