A cross validation analysis evaluating computer model prediction accuracy for a priori planning magnetic resonance-guided laser induced thermal therapy (MRgLITT) procedures in treating focal diseased brain tissue is presented. Two mathematical models are considered. (1) A spectral element discretization of the transient Pennes bioheat transfer equation is implemented to predict the laser induced heating in perfused tissue. (2) A closed-form algorithm for predicting the steady state heat transfer from a linear superposition of analytic point source heating functions is also considered. Prediction accuracy is retrospectively evaluated via leave-one-out cross validation (LOOCV). Modeling predictions are quantitatively evaluated in terms of a Dice similarity coefficient (DSC) between the simulated thermal dose and thermal dose information contained within N = 22 MR thermometry datasets. During LOOCV analysis, the transient model’s DSC mean and median is 0.7323 and 0.8001, respectively, with 15 of 22 DSC values exceeding the success criterion of DSC ≥ 0.7. The steady state model’s DSC mean and median is 0.6431 and 0.6770, respectively, with 10 of 22 passing. A one-sample, one-sided Wilcoxon signed rank test indicates that the transient FEM model achieves the prediction success critera, DSC ≥ 0.7, at a statistically significant level.

Applications must scale well to make efficient use of even medium-scale parallel systems. Because scaling problems are often difficult to diagnose, there is a critical need for scalable tools that guide scientists to the root causes of performance bottlenecks.Although tracing is a powerful performance-analysis technique, tools that employ it can quickly become bottlenecks themselves. Moreover, to obtain actionable performance feedback for modular parallel software systems, it is often necessary to collect and present fine-grained contextsensitive data -the very thing scalable tools avoid. While existing tracing tools can collect calling contexts, they do so only in a coarse-grained fashion; and no prior tool scalably presents both context-and time-sensitive data.This paper describes how to collect, analyze and present fine-grained call path traces for parallel programs. To scale our measurements, we use asynchronous sampling, whose granularity is controlled by a sampling frequency, and a compact representation. To present traces at multiple levels of abstraction and at arbitrary resolutions, we use sampling to render complementary slices of calling-context-sensitive trace data. Because our techniques are general, they can be used on applications that use different parallel programming models (MPI, OpenMP, PGAS). This work is implemented in HPCToolkit.

We present a matrix-free flow solver for high-order finite element discretizations of the incompressible Navier-Stokes and Stokes equations with GPU acceleration. For high polynomial degrees, assembling the matrix for the linear systems resulting from the finite element discretization can be prohibitively expensive, both in terms of computational complexity and memory. For this reason, it is necessary to develop matrix-free operators and preconditioners, which can be used to efficiently solve these linear systems without access to the matrix entries themselves. The matrix-free operator evaluations utilize GPU-accelerated sum-factorization techniques to minimize memory movement and maximize throughput. The preconditioners developed in this work are based on a low-order refined methodology with parallel subspace corrections, as described for diffusion problems in [39]. The saddle-point Stokes system is solved using block-preconditioning techniques, which are robust in mesh size, polynomial degree, time step, and viscosity. For the incompressible Navier-Stokes equations, we make use of projection (fractional step) methods, which require Helmholtz and Poisson solves at each time step. The performance of our flow solvers is assessed on several benchmark problems in two and three spatial dimensions.

The simulation of the transonic buffet phenomenon caused by shock wave and boundary layer interactions is a challenging problem for standard tools in computational fluid dynamics. We present a numerical study of the OAT15A airfoil at Mach number 0.73, angle of attack 3.5 • and Reynolds number 3 × 10 6. In this work, we make use of a wall-resolved implicit large eddy simulation (WRLES) technique using a high-order discontinuous Galerkin discretization. Without making use of subgrid turbulence models or wall models, the WR-LES simulation successfully predicts transonic buffet at an angle of attack of 3.5 •. This method results in good agreement with computational results obtained using detached eddy simulation (DES) method, and fair agreement with experimental results. We study the effect of mesh refinement, polynomial degree, and artificial viscosity parameters on the accuracy of the distribution of the pressure coefficient on the upper surface of the airfoil, and compare both 2D and 3D simulations.

The fully discrete adjoint equations and corresponding adjoint method are derived for unsteady PDE-constrained optimization problems. Specifically, we consider conservation laws on deforming domains that are temporally discretized by high-order fully implicit Runge-Kutta (IRK) schemes. Through a change of variables, the linear systems arising in the primal and dual problem are transformed, leading to computationally cheaper systems that compare competitively with those derived from diagonally implicit Runge-Kutta (DIRK) schemes. Quantities of interest that take the form of space-time integrals are discretized in a solver-consistent manner. Our fully discrete, IRK adjoint method is used to compute exact gradients of quantities of interest with respect to the optimization parameters. These quantities of interest and their gradients are used for gradient-based PDE-constrained optimization. Our implementation of this IRK adjoint method is tested by computing the energetically optimal trajectory of a 2D airfoil in flow governed by the compressible Navier-Stokes equations. We also analyze the parallel performance of our IRK adjoint method and the DIRK adjoint method, showing that our implementation is computationally comparable.