# Choice of iterative solver for a sparse asymmetric matrix with symmetric structure

I have a sparse $$nxn$$ matrix A with pretty interesting structure. It has a block structure with symmetric structure but asymmetric blocks. Expressed mathematically $$A_{jk} = A_{kj}$$ but $$A_{jk} \neq A_{jk}^T$$, so my matrix is not actually symmetric. Are there any algorithms that can take advantage of this kind of system?