822 research outputs found
Unstructured mesh algorithms for aerodynamic calculations
The use of unstructured mesh techniques for solving complex aerodynamic flows is discussed. The principle advantages of unstructured mesh strategies, as they relate to complex geometries, adaptive meshing capabilities, and parallel processing are emphasized. The various aspects required for the efficient and accurate solution of aerodynamic flows are addressed. These include mesh generation, mesh adaptivity, solution algorithms, convergence acceleration, and turbulence modeling. Computations of viscous turbulent two-dimensional flows and inviscid three-dimensional flows about complex configurations are demonstrated. Remaining obstacles and directions for future research are also outlined
Parallel Computation of Nonrigid Image Registration
Automatic intensity-based nonrigid image registration brings significant impact in medical applications such as multimodality fusion of images, serial comparison for monitoring disease progression or regression, and minimally invasive image-guided interventions. However, due to memory and compute intensive nature of the operations, intensity-based image registration has remained too slow to be practical for clinical adoption, with its use limited primarily to as a pre-operative too. Efficient registration methods can lead to new possibilities for development of improved and interactive intraoperative tools and capabilities.
In this thesis, we propose an efficient parallel implementation for intensity-based three-dimensional nonrigid image registration on a commodity graphics processing unit. Optimization techniques are developed to accelerate the compute-intensive mutual information computation. The study is performed on the hierarchical volume subdivision-based algorithm, which is inherently faster than other nonrigid registration algorithms and structurally well-suited for data-parallel computation platforms. The proposed implementation achieves more than 50-fold runtime improvement over a standard implementation on a CPU. The execution time of nonrigid image registration is reduced from hours to minutes while retaining the same level of registration accuracy
A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws
In this article we consider one-dimensional random systems of hyperbolic
conservation laws. We first establish existence and uniqueness of random
entropy admissible solutions for initial value problems of conservation laws
which involve random initial data and random flux functions. Based on these
results we present an a posteriori error analysis for a numerical approximation
of the random entropy admissible solution. For the stochastic discretization,
we consider a non-intrusive approach, the Stochastic Collocation method. The
spatio-temporal discretization relies on the Runge--Kutta Discontinuous
Galerkin method. We derive the a posteriori estimator using continuous
reconstructions of the discrete solution. Combined with the relative entropy
stability framework this yields computable error bounds for the entire
space-stochastic discretization error. The estimator admits a splitting into a
stochastic and a deterministic (space-time) part, allowing for a novel
residual-based space-stochastic adaptive mesh refinement algorithm. We conclude
with various numerical examples investigating the scaling properties of the
residuals and illustrating the efficiency of the proposed adaptive algorithm
Parallel Shooting Sequential Quadratic Programming for Nonlinear MPC Problems
In this paper, we propose a parallel shooting algorithm for solving nonlinear
model predictive control problems using sequential quadratic programming. This
algorithm is built on a two-phase approach where we first test and assess
sequential convergence over many initial trajectories in parallel. However, if
none converge, the algorithm starts varying the Newton step size in parallel
instead. Through this parallel shooting approach, it is expected that the
number of iterations to converge to an optimal solution can be decreased.
Furthermore, the algorithm can be further expanded and accelerated by
implementing it on GPUs. We illustrate the effectiveness of the proposed
Parallel Shooting Sequential Quadratic Programming (PS-SQP) method in some
benchmark examples for nonlinear model predictive control. The developed PS-SQP
parallel solver converges faster on average and especially when significant
nonlinear behaviour is excited in the NMPC horizon.Comment: 7 pages, 6 figures, submitted and accepted for the 7th IEEE
Conference on Control Technology and Applications (CCTA) 202
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