The expertise honed in Patrick’s  Cum Laude distinguished Caltech PhD thesis on

      A Fourier Integral Approach to an Aeolotropic Medium
  
  in 1949  was central to his subsequent construction of particular and complementary solutions to elliptic field equations.

Research conducted during his academic career in UCC ,ably assisted by a long line of graduate students, established the generic nature of these constructions for linear elliptic partial differential equations on regions with sides framing by harmonically varying solutions that decay in the inwards direction.  A convex rectlinear region with sharp or rounded corners is the epitome.

The decomposition of general domains into such sub-regions with the stitching together of their solutions by traditional continuity matching on internal boundaries marked the final chapter of a scientific life well lived.

Much of the development was centered on the Biharmonic plate equation and on Navier's equation of two dimensional elasticity.

The robust computation of fracture coefficients in was a major achievement.  

A reduced software system for solving Laplace's equation was maintained for purposes of presenting the method in its simplest context.

Michael is fortunate to avoid the daunting task of conveying the excitement accompanying the evolution of the method from memory and the deluge of  inherited memorabilia by discovering the testimonial delivered by the late Professor Jim Flavin of Galway to mark the occasion of his 65 birthday following a symposium in his honor in Dublin. His comments on the edge function method are particularly prescient here.

In contrast to younger siblings, teenage memories abound of PMQ at the height of his powers and of the extraordinary bonds that link rising academic stars to their initial group of honour students.

The need of Analog Devices Ireland to compute accurate resistance values for complex thin film resistors in the early nineties was the catalyst that lead to the founding of Edge Function Software with a mission of extending the method to geometries of industrial significance. The field equation governing current flow in thin films is the two dimensional Laplace equation.  The technology for creating a convex decomposition of general polygonal regions appropriate to the method and for knitting element solutions together across the inter-element boundaries was developed by Edge Function Software.  Support for the important activities of  laser trimming and laser cutting was added.