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Large scale parameter estimation problems are among some of the mostcomputationally demanding problems in numerical analysis. An academicresearcher's domain-specific knowledge often precludes that of software design,which results in inversion frameworks that are technically correct, but notscalable to realistically-sized problems. On the other hand, the computationaldemands for realistic problems result in industrial codebases that are gearedsolely for high performance, rather than comprehensibility or flexibility. Wepropose a new software design for inverse problems constrained by partialdifferential equations that bridges the gap between these two seeminglydisparate worlds. A hierarchical and modular design allows a user to delve intoas much detail as she desires, while exploiting high performance primitives atthe lower levels. Our code has the added benefit of actually reflecting theunderlying mathematics of the problem, which lowers the cognitive load on userusing it and reduces the initial startup period before a researcher can befully productive. We also introduce a new preconditioner for the 3D Helmholtzequation that is suitable for fault-tolerant distributed systems. Numericalexperiments on a variety of 2D and 3D test problems demonstrate theeffectiveness of this approach on scaling algorithms from small to large scaleproblems with minimal code changes.

A Unified 2D/3D Large Scale Software Environment for Nonlinear Inverse Problems