The solution of linear systems of equations that arise when singularly perturbed partial differential equations are discretized can be difficult: direct solvers scale poorly, but are also known not to be robust with respect to the perturbation parameter, while the design of parameter robust preconditioners is not trivial, primarily due to the specialised layer adapted meshes used for such problems [MacLachlan and Madden, 2013]. Here we present a multigrid solver strategy that circumvents this problem by using a robust patched mesh method [de Falca and O'Riordan, 2009], as well as permitting parallelization. Numerical results demonstrate the efficiency of the method.

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