Non-destructive evaluation of structural components is critical for reducing costs from unnecessary replacements and maintenance. We study the utility of a non-contact modality for the inspection of thin metal plates for the presence of through cracks. Sensitivity to early stages of deterioration allows for simpler and less expensive repair than if a flaw propagates and becomes more damaging. Hence, we focus on the characterization of very small cracks with a thermal imaging technique. Through cracks interact with the flow of heat within a component, so that the characterization of cracks from a thermal image amounts to solving an inverse problem to discover unknown parameters that describe the crack. We consider cracks with length of less than a millimeter, falling under the pixel resolution of the recording thermal camera. Although these flaws are not directly visible from imaging data, the well-understood theory of heat conduction can be used in inference of crack properties. Herein we present a method to design an inspection modality that yields optimal data for such inference. Numerical experiments are performed to compare our optimized inspection setup to previous thermographic inspection scenarios found in the literature. Our design is found to produce the same quality of inference as these previous experiments which require much more expensive equipment (e.g. more powerful lasers and more sensitive IR cameras).

The simulation of heat flow through heterogeneous material is important for the design of structural and electronic components. Classical analytical solutions to the heat equation PDE are not known for many such domains, even those having simple geometries. The finite element method can provide approximations to a weak form continuum solution, with increasing accuracy as the number of degrees of freedom in the model increases. This comes at a cost of increased memory usage and computation time; even when taking advantage of sparse matrix techniques for the finite element system matrix. We summarize recent approaches in solving problems in structural mechanics and steady state heat conduction which do not require the explicit assembly of any system matrices, and adapt them to a method for solving the time-depended flow of heat. These approaches are highly parallelizable, and can be performed on graphical processing units (GPUs). Furthermore, they lend themselves to the simulation of heterogeneous material, with a minimum of added complexity. We present the mathematical framework of assembly-free FEM approaches, through which we summarize the benefits of GPU computation. We discuss our implementation using the OpenCL computing framework, and show how it is further adapted for use on multiple GPUs. We compare the performance of single and dual GPUs implementations of our method with previous GPU computing strategies from the literature and a CPU sparse matrix approach. The utility of the novel method is demonstrated through the solution of a real-world coefficient inverse problem that requires thousands of transient heat flow simulations, each of which involves solving a 1 million degree of freedom linear system over hundreds of time steps.

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