function V1 = laplaceStepJacobiPBC(V1,V0)
%V1 = laplaceStepJacobiPBC(V0);
% assumes that B.C. specify V on the exterior edges in 2D

% handle first row using periodic BC
for jj = 2:size(V0,2)-1
    V1(1,jj) = ...
        (V0(2,jj) + V0(end,jj) + V0(1,jj+1) + V0(1,jj-1))/4;
end

for ii = 2:size(V0,1)-1
    for jj = 2:size(V0,2)-1
        V1(ii,jj) = ...
            (V0(ii+1,jj) + V0(ii-1,jj) + V0(ii,jj+1) + V0(ii,jj-1))/4;
    end
end

% handle last row using periodic BC
for jj = 2:size(V0,2)-1
    V1(end,jj) = ...
        (V0(1,jj) + V0(end-1,jj) + V0(end,jj+1) + V0(end,jj-1))/4;
end

return