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Scientific Computing

Numerical simulation of real-world phenomena provides fertile ground for building interdisciplinary relationships. The SCI Institute has a long tradition of building these relationships in a win-win fashion – a win for the theoretical and algorithmic development of numerical modeling and simulation techniques and a win for the discipline-specific science of interest. High-order and adaptive methods, uncertainty quantification, complexity analysis, and parallelization are just some of the topics being investigated by SCI faculty. These areas of computing are being applied to a wide variety of engineering applications ranging from fluid mechanics and solid mechanics to bioelectricity.


Martin Berzins

Parallel Computing

Mike Kirby

Finite Element Methods
Uncertainty Quantification

Valerio Pascucci

Scientific Data Management

Chris Johnson

Problem Solving Environments

Ross Whitaker


Chuck Hansen


Scientific Computing Project Sites:

Publications in Scientific Computing:

Lateral ventricle morphology analysis via mean latitude axis
B. Paniagua, A. Lyall, J.-B. Berger, C. Vachet, R.M. Hamer, S. Woolson, W. Lin, J. Gilmore, M. Styner. In Proceedings of SPIE 8672, Biomedical Applications in Molecular, Structural, and Functional Imaging, 86720M, 2013.
DOI: 10.1117/12.2006846
PubMed ID: 23606800
PubMed Central ID: PMC3630372

Statistical shape analysis has emerged as an insightful method for evaluating brain structures in neuroimaging studies, however most shape frameworks are surface based and thus directly depend on the quality of surface alignment. In contrast, medial descriptions employ thickness information as alignment-independent shape metric. We propose a joint framework that computes local medial thickness information via a mean latitude axis from the well-known spherical harmonic (SPHARM-PDM) shape framework. In this work, we applied SPHARM derived medial representations to the morphological analysis of lateral ventricles in neonates. Mild ventriculomegaly (MVM) subjects are compared to healthy controls to highlight the potential of the methodology. Lateral ventricles were obtained from MRI scans of neonates (9- 144 days of age) from 30 MVM subjects as well as age- and sex-matched normal controls (60 total). SPHARM-PDM shape analysis was extended to compute a mean latitude axis directly from the spherical parameterization. Local thickness and area was straightforwardly determined. MVM and healthy controls were compared using local MANOVA and compared with the traditional SPHARM-PDM analysis. Both surface and mean latitude axis findings differentiate successfully MVM and healthy lateral ventricle morphology. Lateral ventricles in MVM neonates show enlarged shapes in tail and head. Mean latitude axis is able to find significant differences all along the lateral ventricle shape, demonstrating that local thickness analysis provides significant insight over traditional SPHARM-PDM. This study is the first to precisely quantify 3D lateral ventricle morphology in MVM neonates using shape analysis.

Modeling 4D changes in pathological anatomy using domain adaptation: analysis of TBI imaging using a tumor database
Bo Wang, M. Prastawa, A. Saha, S.P. Awate, A. Irimia, M.C. Chambers, P.M. Vespa, J.D. Van Horn, V. Pascucci, G. Gerig. In Proceedings of the 2013 MICCAI-MBIA Workshop, Lecture Notes in Computer Science (LNCS), Vol. 8159, Note: Awarded Best Paper!, pp. 31--39. 2013.
DOI: 10.1007/978-3-319-02126-3_4

Analysis of 4D medical images presenting pathology (i.e., lesions) is signi cantly challenging due to the presence of complex changes over time. Image analysis methods for 4D images with lesions need to account for changes in brain structures due to deformation, as well as the formation and deletion of new structures (e.g., edema, bleeding) due to the physiological processes associated with damage, intervention, and recovery. We propose a novel framework that models 4D changes in pathological anatomy across time, and provides explicit mapping from a healthy template to subjects with pathology. Moreover, our framework uses transfer learning to leverage rich information from a known source domain, where we have a collection of completely segmented images, to yield effective appearance models for the input target domain. The automatic 4D segmentation method uses a novel domain adaptation technique for generative kernel density models to transfer information between different domains, resulting in a fully automatic method that requires no user interaction. We demonstrate the effectiveness of our novel approach with the analysis of 4D images of traumatic brain injury (TBI), using a synthetic tumor database as the source domain.

Investigating Applications Portability with the Uintah DAG-based Runtime System on PetaScale Supercomputers
SCI Technical Report, Q. Meng, A. Humphrey, J. Schmidt, M. Berzins. No. UUSCI-2013-003, SCI Institute, University of Utah, 2013.

Present trends in high performance computing present formidable challenges for applications code using multicore nodes possibly with accelerators and/or co-processors and reduced memory while still attaining scalability. Software frameworks that execute machineindependent applications code using a runtime system that shields users from architectural complexities offer a possible solution. The Uintah framework for example, solves a broad class of large-scale problems on structured adaptive grids using fluid-flow solvers coupled with particle-based solids methods. Uintah executes directed acyclic graphs of computational tasks with a scalable asynchronous and dynamic runtime system for CPU cores and/or accelerators/coprocessors on a node. Uintah's clear separation between application and runtime code has led to scalability increases of 1000x without significant changes to application code. This methodology is tested on three leading Top500 machines; OLCF Titan, TACC Stampede and ALCF Mira using three diverse and challenging applications problems. This investigation of scalability with regard to the different processors and communications performance leads to the overall conclusion that the adaptive DAG-based approach provides a very powerful abstraction for solving challenging multiscale multi-physics engineering problems on some of the largest and most powerful computers available today.

Keywords: Uintah, hybrid parallelism, scalability, parallel, adaptive, MIC, Xeon Phi, heterogeneous systems, Stampede, co-processor

A new discrete element analysis method for predicting hip joint contact stresses
C.L. Abraham, S.A. Maas, J.A. Weiss, B.J. Ellis, C.L. Peters, A.E. Anderson. In Journal of Biomechanics, Vol. 46, No. 6, pp. 1121--1127. 2013.
DOI: 10.1016/j.jbiomech.2013.01.012

Quantifying cartilage contact stress is paramount to understanding hip osteoarthritis. Discrete element analysis (DEA) is a computationally efficient method to estimate cartilage contact stresses. Previous applications of DEA have underestimated cartilage stresses and yielded unrealistic contact patterns because they assumed constant cartilage thickness and/or concentric joint geometry. The study objectives were to: (1) develop a DEA model of the hip joint with subject-specific bone and cartilage geometry, (2) validate the DEA model by comparing DEA predictions to those of a validated finite element analysis (FEA) model, and (3) verify both the DEA and FEA models with a linear-elastic boundary value problem. Springs representing cartilage in the DEA model were given lengths equivalent to the sum of acetabular and femoral cartilage thickness and gap distance in the FEA model. Material properties and boundary/loading conditions were equivalent. Walking, descending, and ascending stairs were simulated. Solution times for DEA and FEA models were ∼7 s and ∼65 min, respectively. Irregular, complex contact patterns predicted by DEA were in excellent agreement with FEA. DEA contact areas were 7.5%, 9.7% and 3.7% less than FEA for walking, descending stairs, and ascending stairs, respectively. DEA models predicted higher peak contact stresses (9.8–13.6 MPa) and average contact stresses (3.0–3.7 MPa) than FEA (6.2–9.8 and 2.0–2.5 MPa, respectively). DEA overestimated stresses due to the absence of the Poisson's effect and a direct contact interface between cartilage layers. Nevertheless, DEA predicted realistic contact patterns when subject-specific bone geometry and cartilage thickness were used. This DEA method may have application as an alternative to FEA for pre-operative planning of joint-preserving surgery such as acetabular reorientation during peri-acetabular osteotomy.

Three-dimensional Quantification of Femoral Head Shape in Controls and Patients with Cam-type Femoroacetabular Impingement
M.D. Harris, S.P. Reese, C.L. Peters, J.A. Weiss, A.E. Anderson. In Annals of Biomedical Engineering, Vol. 41, No. 6, pp. 1162--1171. 2013.
DOI: 10.1007/s10439-013-0762-1

An objective measurement technique to quantify 3D femoral head shape was developed and applied to normal subjects and patients with cam-type femoroacetabular impingement (FAI). 3D reconstructions were made from high-resolution CT images of 15 cam and 15 control femurs. Femoral heads were fit to ideal geometries consisting of rotational conchoids and spheres. Geometric similarity between native femoral heads and ideal shapes was quantified. The maximum distance native femoral heads protruded above ideal shapes and the protrusion area were measured. Conchoids provided a significantly better fit to native femoral head geometry than spheres for both groups. Cam-type FAI femurs had significantly greater maximum deviations (4.99 ± 0.39 mm and 4.08 ± 0.37 mm) than controls (2.41 ± 0.31 mm and 1.75 ± 0.30 mm) when fit to spheres or conchoids, respectively. The area of native femoral heads protruding above ideal shapes was significantly larger in controls when a lower threshold of 0.1 mm (for spheres) and 0.01 mm (for conchoids) was used to define a protrusion. The 3D measurement technique described herein could supplement measurements of radiographs in the diagnosis of cam-type FAI. Deviations up to 2.5 mm from ideal shapes can be expected in normal femurs while deviations of 4–5 mm are characteristic of cam-type FAI.

Synergistic Challenges in Data-Intensive Science and Exascale Computing
J. Chen, A. Choudhary, S. Feldman, B. Hendrickson, C.R. Johnson, R. Mount, V. Sarkar, V. White, D. Williams. Note: Summary Report of the Advanced Scientific Computing Advisory Committee (ASCAC) Subcommittee, March, 2013.

The ASCAC Subcommittee on Synergistic Challenges in Data-Intensive Science and Exascale Computing has reviewed current practice and future plans in multiple science domains in the context of the challenges facing both Big Data and the Exascale Computing. challenges. The review drew from public presentations, workshop reports and expert testimony. Data-intensive research activities are increasing in all domains of science, and exascale computing is a key enabler of these activities. We briefly summarize below the key findings and recommendations from this report from the perspective of identifying investments that are most likely to positively impact both data-intensive science goals and exascale computing goals.

Preliminary Experiences with the Uintah Framework on Intel Xeon Phi and Stampede
SCI Technical Report, Q. Meng, A. Humphrey, J. Schmidt, M. Berzins. No. UUSCI-2013-002, SCI Institute, University of Utah, 2013.

In this work, we describe our preliminary experiences on the Stampede system in the context of the Uintah Computational Framework. Uintah was developed to provide an environment for solving a broad class of fluid-structure interaction problems on structured adaptive grids. Uintah uses a combination of fluid-flow solvers and particle-based methods, together with a novel asynchronous taskbased approach and fully automated load balancing. While we have designed scalable Uintah runtime systems for large CPU core counts, the emergence of heterogeneous systems presents considerable challenges in terms of effectively utilizing additional on-node accelerators and co-processors, deep memory hierarchies, as well as managing multiple levels of parallelism. Our recent work has addressed the emergence of heterogeneous CPU/GPU systems with the design of a Unified heterogeneous runtime system, enabling Uintah to fully exploit these architectures with support for asynchronous, out-of-order scheduling of both CPU and GPU computational tasks. Using this design, Uintah has run at full scale on the Keeneland System and TitanDev. With the release of the Intel Xeon Phi co-processor and the recent availability of the Stampede system, we show that Uintah may be modified to utilize such a coprocessor based system. We also explore the different usage models provided by the Xeon Phi with the aim of understanding portability of a general purpose framework like Uintah to this architecture. These usage models range from the pragma based offload model to the more complex symmetric model, utilizing all co-processor and host CPU cores simultaneously. We provide preliminary results of the various usage models for a challenging adaptive mesh refinement problem, as well as a detailed account of our experience adapting Uintah to run on the Stampede system. Our conclusion is that while the Stampede system is easy to use, obtaining high performance from the Xeon Phi co-processors requires a substantial but different investment to that needed for GPU-based systems.

Keywords: Uintah, hybrid parallelism, scalability, parallel, adaptive, MIC, Xeon Phi, heterogeneous systems, Stampede, co-processor

Applying high-performance computing to petascale explosive simulations
J.R. Peterson, C.A. Wight, M. Berzins. In Procedia Computer Science, 2013.

Hazardous scenarios involving explosives are difficult to experimentally study and simulation is often the only viable approach to study highly reactive phenomena. Explosive simulations are computationally expensive, requiring supercomputing resources for continued scientific discovery in the field. Here an idealized mesoscale simulation of explosive grains under mechanical insult by a high-speed projectile with reaction represented by a novel kinetic model is designed to test the scalability of the Uintah software on petascale supercomputers. Good scalability is found up to 49K processors. Timing breakdown of computational tasks are determined with relocation of Lagrangian particles and interpolation of those particles to the grid identified as the most expensive operation and ideal for optimization. Potential optimization strategies are identified. Realistic model simulations rather than toy model simulations are found to better represent scalability of a science code on a supercomputer. Estimations for total supercomputer hours necessary to complete the kinetic model validation study are reported.

Keywords: Energetic Material Hazards, Uintah, MPM, ICE, MPMICE, Scalable Parallelism, C-SAFE

Crash Early, Crash Often, Explain Well: Practical Formal Correctness Checking of Million-core Problem Solving Environments for HPC
D.C.B. de Oliveira, Z. Rakamaric, G. Gopalakrishnan, A. Humphrey, Q. Meng, M. Berzins. In Proceedings of the 35th International Conference on Software Engineering (ICSE 2013), pp. (accepted). 2013.

While formal correctness checking methods have been deployed at scale in a number of important practical domains, we believe that such an experiment has yet to occur in the domain of high performance computing at the scale of a million CPU cores. This paper presents preliminary results from the Uintah Runtime Verification (URV) project that has been launched with this objective. Uintah is an asynchronous task-graph based problem-solving environment that has shown promising results on problems as diverse as fluid-structure interaction and turbulent combustion at well over 200K cores to date. Uintah has been tested on leading platforms such as Kraken, Keenland, and Titan consisting of multicore CPUs and GPUs, incorporates several innovative design features, and is following a roadmap for development well into the million core regime. The main results from the URV project to date are crystallized in two observations: (1) A diverse array of well-known ideas from lightweight formal methods and testing/observing HPC systems at scale have an excellent chance of succeeding. The real challenges are in finding out exactly which combinations of ideas to deploy, and where. (2) Large-scale problem solving environments for HPC must be designed such that they can be \"crashed early\" (at smaller scales of deployment) and \"crashed often\" (have effective ways of input generation and schedule perturbation that cause vulnerabilities to be attacked with higher probability). Furthermore, following each crash, one must \"explain well\" (given the extremely obscure ways in which an error finally manifests itself, we must develop ways to record information leading up to the crash in informative ways, to minimize offsite debugging burden). Our plans to achieve these goals and to measure our success are described. We also highlight some of the broadly applicable concepts and approaches.

Keywords: Uintah

Past, Present, and Future Scalability of the Uintah Software
M. Berzins, J. Schmidt, Q. Meng, A. Humphrey. In Proceedings of the Blue Waters Extreme Scaling Workshop 2012, pp. Article No.: 6. 2013.

The past, present and future scalability of the Uintah Software framework is considered with the intention of describing a successful approach to large scale parallelism and also considering how this approach may need to be extended for future architectures. Uintah allows the solution of large scale fluid-structure interaction problems through the use of fluid flow solvers coupled with particle-based solids methods. In addition Uintah uses a combustion solver to tackle a broad and challenging class of turbulent combustion problems. A unique feature of Uintah is that it uses an asynchronous task-based approach with automatic load balancing to solve complex problems using techniques such as adaptive mesh refinement. At present, Uintah is able to make full use of present-day massively parallel machines as the result of three phases of development over the past dozen years. These development phases have led to an adaptive scalable run-time system that is capable of independently scheduling tasks to multiple CPUs cores and GPUs on a node. In the case of solving incompressible low-mach number applications it is also necessary to use linear solvers and to consider the challenges of radiation problems. The approaches adopted to achieve present scalability are described and their extensions to possible future architectures is considered.

Keywords: netl, Uintah, parallelism, scalability, adaptive mesh refinement, linear equations

Data and Range-Bounded Polynomials in ENO Methods
M. Berzins. In Journal of Computational Science, Vol. 4, No. 1-2, pp. 62--70. 2013.
DOI: 10.1016/j.jocs.2012.04.006

Essentially Non-Oscillatory (ENO) methods and Weighted Essentially Non-Oscillatory (WENO) methods are of fundamental importance in the numerical solution of hyperbolic equations. A key property of such equations is that the solution must remain positive or lie between bounds. A modification of the polynomials used in ENO methods to ensure that the modified polynomials are either bounded by adjacent values (data-bounded) or lie within a specified range (range-bounded) is considered. It is shown that this approach helps both in the range boundedness in the preservation of extrema in the ENO polynomial solution.

Effect of deltoid tension and humeral version in reverse total shoulder arthroplasty: a biomechanical study
H.B. Henninger, Barg A, A.E. Anderson, K.N. Bachus, R.Z. Tashjian, R.T. Burks. In Journal of Shoulder and Elbow Surgery, Vol. 21, No. 4, pp. 483–-490. 2012.
DOI: 10.1016/j.jse.2011.01.040

No clear recommendations exist regarding optimal humeral component version and deltoid tension in reverse total shoulder arthroplasty (TSA).

Materials and methods
A biomechanical shoulder simulator tested humeral versions (0°, 10°, 20° retroversion) and implant thicknesses (-3, 0, +3 mm from baseline) after reverse TSA in human cadavers. Abduction and external rotation ranges of motion as well as abduction and dislocation forces were quantified for native arms and arms implanted with 9 combinations of humeral version and implant thickness.

Resting abduction angles increased significantly (up to 30°) after reverse TSA compared with native shoulders. With constant posterior cuff loads, native arms externally rotated 20°, whereas no external rotation occurred in implanted arms (20° net internal rotation). Humeral version did not affect rotational range of motion but did alter resting abduction. Abduction forces decreased 30% vs native shoulders but did not change when version or implant thickness was altered. Humeral center of rotation was shifted 17 mm medially and 12 mm inferiorly after implantation. The force required for lateral dislocation was 60% less than anterior and was not affected by implant thickness or version.

Reverse TSA reduced abduction forces compared with native shoulders and resulted in limited external rotation and abduction ranges of motion. Because abduction force was reduced for all implants, the choice of humeral version and implant thickness should focus on range of motion. Lateral dislocation forces were less than anterior forces; thus, levering and inferior/posterior impingement may be a more probable basis for dislocation (laterally) than anteriorly directed forces.

Keywords: Shoulder, reverse arthroplasty, deltoid tension, humeral version, biomechanical simulator

Extreme-Scale Visual Analytics
P.C. Wong, H. Shen, V. Pascucci. In IEEE Computer Graphics and Applications, Vol. 32, No. 4, pp. 23--25. 2012.
DOI: 10.1109/MCG.2012.73

Extreme-scale visual analytics (VA) is about applying VA to extreme-scale data. The articles in this special issue examine advances related to extreme-scale VA problems, their analytical and computational challenges, and their real-world applications.

Atrial Fibrosis Quantified Using Late Gadolinium Enhancement MRI is AssociatedWith Sinus Node Dysfunction Requiring Pacemaker Implant
N.W. Akoum, C.J. McGann, G. Vergara, T. Badger, R. Ranjan, C. Mahnkopf, E.G. Kholmovski, R.S. Macleod, N.F. Marrouche. In Journal of Cardiovascular Electrophysiology, Vol. 23, No. 1, pp. 44--50. 2012.
DOI: 10.1111/j.1540-8167.2011.02140.x

Atrial Fibrosis and Sinus Node Dysfunction. Introduction: Sinus node dysfunction (SND) commonly manifests with atrial arrhythmias alternating with sinus pauses and sinus bradycardia. The underlying process is thought to be because of atrial fibrosis. We assessed the value of atrial fibrosis, quantified using Late Gadolinium Enhanced-MRI (LGE-MRI), in predicting significant SND requiring pacemaker implant.

Methods: Three hundred forty-four patients with atrial fibrillation (AF) presenting for catheter ablation underwent LGE-MRI. Left atrial (LA) fibrosis was quantified in all patients and right atrial (RA) fibrosis in 134 patients. All patients underwent catheter ablation with pulmonary vein isolation with posterior wall and septal debulking. Patients were followed prospectively for 329 ± 245 days. Ambulatory monitoring was instituted every 3 months. Symptomatic pauses and bradycardia were treated with pacemaker implantation per published guidelines.

Results: The average patient age was 65 ± 12 years. The average wall fibrosis was 16.7 ± 11.1% in the LA, and 5.3 ± 6.4% in the RA. RA fibrosis was correlated with LA fibrosis (R2= 0.26; P < 0.01). Patients were divided into 4 stages of LA fibrosis (Utah I: 35%). Twenty-two patients (mean atrial fibrosis, 23.9%) required pacemaker implantation during follow-up. Univariate and multivariate analysis identified LA fibrosis stage (OR, 2.2) as a significant predictor for pacemaker implantation with an area under the curve of 0.704.

Conclusions: In patients with AF presenting for catheter ablation, LGE-MRI quantification of atrial fibrosis demonstrates preferential LA involvement. Significant atrial fibrosis is associated with clinically significant SND requiring pacemaker implantation. (J Cardiovasc Electrophysiol, Vol. 23, pp. 44-50, January 2012)

30 Generation of Cloned Transgenic Goats with Cardiac Specific Overexpression of Transforming Growth Factor β1
Q. Meng, J. Hall, H. Rutigliano, X. Zhou, B.R. Sessions, R. Stott, K. Panter, C.J. Davies, R. Ranjan, D. Dosdall, R.S. MacLeod, N. Marrouche, K.L. White, Z. Wang, I.A. Polejaeva. In Reproduction, Fertility and Development, Vol. 25, No. 1, pp. 162--163. 2012.
DOI: 10.1071/RDv25n1Ab30

Transforming growth factor β1 (TGF-β1) has a potent profibrotic function and is central to signaling cascades involved in interstitial fibrosis, which plays a critical role in the pathobiology of cardiomyopathy and contributes to diastolic and systolic dysfunction. In addition, fibrotic remodeling is responsible for generation of re-entry circuits that promote arrhythmias (Bujak and Frangogiannis 2007 Cardiovasc. Res. 74, 184–195). Due to the small size of the heart, functional electrophysiology of transgenic mice is problematic. Large transgenic animal models have the potential to offer insights into conduction heterogeneity associated with fibrosis and the role of fibrosis in cardiovascular diseases. The goal of this study was to generate transgenic goats overexpressing an active form of TGFβ-1 under control of the cardiac-specific α-myosin heavy chain promoter (α-MHC). A pcDNA3.1DV5-MHC-TGF-β1cys33ser vector was constructed by subcloning the MHC-TGF-β1 fragment from the plasmid pUC-BM20-MHC-TGF-β1 (Nakajima et al. 2000 Circ. Res. 86, 571–579) into the pcDNA3.1D V5 vector. The Neon transfection system was used to electroporate primary goat fetal fibroblasts. After G418 selection and PCR screening, transgenic cells were used for SCNT. Oocytes were collected by slicing ovaries from an abattoir and matured in vitro in an incubator with 5\% CO2 in air. Cumulus cells were removed at 21 to 23 h post-maturation. Oocytes were enucleated by aspirating the first polar body and nearby cytoplasm by micromanipulation in Hepes-buffered SOF medium with 10 µg of cytochalasin B mL–1. Transgenic somatic cells were individually inserted into the perivitelline space and fused with enucleated oocytes using double electrical pulses of 1.8 kV cm–1 (40 µs each). Reconstructed embryos were activated by ionomycin (5 min) and DMAP and cycloheximide (CHX) treatments. Cloned embryos were cultured in G1 medium for 12 to 60 h in vitro and then transferred into synchronized recipient females. Pregnancy was examined by ultrasonography on day 30 post-transfer. A total of 246 cloned embryos were transferred into 14 recipients that resulted in production of 7 kids. The pregnancy rate was higher in the group cultured for 12 h compared with those cultured 36 to 60 h [44.4\% (n = 9) v. 20\% (n = 5)]. The kidding rates per embryo transferred of these 2 groups were 3.8\% (n = 156) and 1.1\% (n = 90), respectively. The PCR results confirmed that all the clones were transgenic. Phenotype characterization [e.g. gene expression, electrocardiogram (ECG), and magnetic resonance imaging (MRI)] is underway. We demonstrated successful production of transgenic goat via SCNT. To our knowledge, this is the first transgenic goat model produced for cardiovascular research.

Stochastic Collocation for Optimal Control Problems with Stochastic PDE Constraints
H. Tiesler, R.M. Kirby, D. Xiu, T. Preusser. In SIAM Journal on Control and Optimization, Vol. 50, No. 5, pp. 2659--2682. 2012.
DOI: 10.1137/110835438

We discuss the use of stochastic collocation for the solution of optimal control problems which are constrained by stochastic partial differential equations (SPDE). Thereby the constraining, SPDE depends on data which is not deterministic but random. Assuming a deterministic control, randomness within the states of the input data will propagate to the states of the system. For the solution of SPDEs there has recently been an increasing effort in the development of efficient numerical schemes based upon the mathematical concept of generalized polynomial chaos. Modal-based stochastic Galerkin and nodal-based stochastic collocation versions of this methodology exist, both of which rely on a certain level of smoothness of the solution in the random space to yield accelerated convergence rates. In this paper we apply the stochastic collocation method to develop a gradient descent as well as a sequential quadratic program (SQP) for the minimization of objective functions constrained by an SPDE. The stochastic function involves several higher-order moments of the random states of the system as well as classical regularization of the control. In particular we discuss several objective functions of tracking type. Numerical examples are presented to demonstrate the performance of our new stochastic collocation minimization approach.

Keywords: stochastic collocation, optimal control, stochastic partial differential equations

Lattice Cleaving: Conforming Tetrahedral Meshes of Multimaterial Domains with Bounded Quality
J.R. Bronson, J.A. Levine, R.T. Whitaker. In Proceedings of the 21st International Meshing Roundtable, pp. 191--209. 2012.

We introduce a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials. The proposed method allows for an arbitrary number of materials, produces high-quality tetrahedral meshes with upper and lower bounds on dihedral angles, and guarantees geometric delity. Moreover, the method is combinatoric so its implementation enables rapid mesh construction. These meshes are structured in a way that also allows grading, in order to reduce element counts in regions of homogeneity.

Efficient data restructuring and aggregation for I/O acceleration in PIDX
S. Kumar, V. Vishwanath, P. Carns, J.A. Levine, R. Latham, G. Scorzelli, H. Kolla, R. Grout, R. Ross, M.E. Papka, J. Chen, V. Pascucci. In Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, IEEE Computer Society Press, pp. 50:1--50:11. 2012.
ISBN: 978-1-4673-0804-5

Hierarchical, multiresolution data representations enable interactive analysis and visualization of large-scale simulations. One promising application of these techniques is to store high performance computing simulation output in a hierarchical Z (HZ) ordering that translates data from a Cartesian coordinate scheme to a one-dimensional array ordered by locality at different resolution levels. However, when the dimensions of the simulation data are not an even power of 2, parallel HZ ordering produces sparse memory and network access patterns that inhibit I/O performance. This work presents a new technique for parallel HZ ordering of simulation datasets that restructures simulation data into large (power of 2) blocks to facilitate efficient I/O aggregation. We perform both weak and strong scaling experiments using the S3D combustion application on both Cray-XE6 (65,536 cores) and IBM Blue Gene/P (131,072 cores) platforms. We demonstrate that data can be written in hierarchical, multiresolution format with performance competitive to that of native data-ordering methods.

Extending the SCIRun Problem Solving Environment to Large-Scale Applications
J. Knezevic, R.-P. Mundani, E. Rank, A. Khan, C.R. Johnson. In Proceedings of Applied Computing 2012, IADIS, pp. 171--178. October, 2012.

To make the most of current advanced computing technologies, experts in particular areas of science and engineering should be supported by sophisticated tools for carrying out computational experiments. The complexity of individual components of such tools should be hidden from them so they may concentrate on solving the specific problem within their field of expertise. One class of such tools are Problem Solving Environments (PSEs). The contribution of this paper refers to the idea of integration of an interactive computing framework applicable to different engineering applications into the SCIRun PSE in order to enable interactive real-time response of the computational model to user interaction even for large-scale problems. While the SCIRun PSE allows for real-time computational steering, we propose extending this functionality to a wider range of applications and larger scale problems. With only minor code modifications the proposed system allows each module scheduled for execution in a dataflow-based simulation to be automatically interrupted and re-scheduled. This rescheduling allows one to keep the relation between the user interaction and its immediate effect transparent independent of the problem size, thus, allowing for the intuitive and interactive exploration of simulation results.

Keywords: scirun

Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering for discontinuous Galerkin Solutions: Improved Errors Versus Higher-Order Accuracy
J. King, H. Mirzaee, J.K. Ryan, R.M. Kirby. In Journal of Scientific Computing, Vol. 53, pp. 129--149. 2012.
DOI: 10.1007/s10915-012-9593-8

Smoothness-increasing accuracy-conserving (SIAC) filtering has demonstrated its effectiveness in raising the convergence rate of discontinuous Galerkin solutions from order k + 1/2 to order 2k + 1 for specific types of translation invariant meshes (Cockburn et al. in Math. Comput. 72:577–606, 2003; Curtis et al. in SIAM J. Sci. Comput. 30(1):272– 289, 2007; Mirzaee et al. in SIAM J. Numer. Anal. 49:1899–1920, 2011). Additionally, it improves the weak continuity in the discontinuous Galerkin method to k - 1 continuity. Typically this improvement has a positive impact on the error quantity in the sense that it also reduces the absolute errors. However, not enough emphasis has been placed on the difference between superconvergent accuracy and improved errors. This distinction is particularly important when it comes to understanding the interplay introduced through meshing, between geometry and filtering. The underlying mesh over which the DG solution is built is important because the tool used in SIAC filtering—convolution—is scaled by the geometric mesh size. This heavily contributes to the effectiveness of the post-processor. In this paper, we present a study of this mesh scaling and how it factors into the theoretical errors. To accomplish the large volume of post-processing necessary for this study, commodity streaming multiprocessors were used; we demonstrate for structured meshes up to a 50× speed up in the computational time over traditional CPU implementations of the SIAC filter.