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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

Martin Berzins

Parallel Computing
GPUs
mike

Mike Kirby

Finite Element Methods
Uncertainty Quantification
GPUs
pascucci

Valerio Pascucci

Scientific Data Management
chris

Chris Johnson

Problem Solving Environments
ross

Ross Whitaker

GPUs
chuck

Chuck Hansen

GPUs
   

Scientific Computing Project Sites:


Publications in Scientific Computing:


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.



Multiscale Modeling of High Explosives for Transportation Accidents
J.R. Peterson, J.C. Beckvermit, T. Harman, M. Berzins, C.A. Wight. In Proceedings of the 1st Conference of the Extreme Science and Engineering Discovery Environment: Bridging from the eXtreme to the campus and beyond, 2012.
DOI: 10.1145/2335755.2335828

The development of a reaction model to simulate the accidental detonation of a large array of seismic boosters in a semi-truck subject to fire is considered. To test this model large scale simulations of explosions and detonations were performed by leveraging the massively parallel capabilities of the Uintah Computational Framework and the XSEDE computational resources. Computed stress profiles in bulk-scale explosive materials were validated using compaction simulations of hundred micron scale particles and found to compare favorably with experimental data. A validation study of reaction models for deflagration and detonation showed that computational grid cell sizes up to 10 mm could be used without loss of fidelity. The Uintah Computational Framework shows linear scaling up to 180K cores which combined with coarse resolution and validated models will now enable simulations of semi-truck scale transportation accidents for the first time.



Radiation Modeling Using the Uintah Heterogeneous CPU/GPU Runtime System
A. Humphrey, Q. Meng, M. Berzins, T. Harman. In Proceedings of the first conference of the Extreme Science and Engineering Discovery Environment (XSEDE'12), Association for Computing Machinery, 2012.
DOI: 10.1145/2335755.2335791

The Uintah Computational Framework was developed to provide an environment for solving fluid-structure interaction problems on structured adaptive grids on large-scale, long-running, data-intensive problems. Uintah uses a combination of fluid-flow solvers and particle-based methods for solids, together with a novel asynchronous task-based approach with fully automated load balancing. Uintah demonstrates excellent weak and strong scalability at full machine capacity on XSEDE resources such as Ranger and Kraken, and through the use of a hybrid memory approach based on a combination of MPI and Pthreads, Uintah now runs on up to 262k cores on the DOE Jaguar system. In order to extend Uintah to heterogeneous systems, with ever-increasing CPU core counts and additional onnode GPUs, a new dynamic CPU-GPU task scheduler is designed and evaluated in this study. This new scheduler enables Uintah to fully exploit these architectures with support for asynchronous, outof- order scheduling of both CPU and GPU computational tasks. A new runtime system has also been implemented with an added multi-stage queuing architecture for efficient scheduling of CPU and GPU tasks. This new runtime system automatically handles the details of asynchronous memory copies to and from the GPU and introduces a novel method of pre-fetching and preparing GPU memory prior to GPU task execution. In this study this new design is examined in the context of a developing, hierarchical GPUbased ray tracing radiation transport model that provides Uintah with additional capabilities for heat transfer and electromagnetic wave propagation. The capabilities of this new scheduler design are tested by running at large scale on the modern heterogeneous systems, Keeneland and TitanDev, with up to 360 and 960 GPUs respectively. On these systems, we demonstrate significant speedups per GPU against a standard CPU core for our radiation problem.

Keywords: Uintah, hybrid parallelism, scalability, parallel, adaptive, GPU, heterogeneous systems, Keeneland, TitanDev



Radiation Modeling Using the Uintah Heterogeneous CPU/GPU Runtime System
SCI Technical Report, A. Humphrey, Q. Meng, M. Berzins, T. Harman. No. UUSCI-2012-003, SCI Institute, University of Utah, 2012.

The Uintah Computational Framework was developed to provide an environment for solving fluid-structure interaction problems on structured adaptive grids on large-scale, long-running, data-intensive problems. Uintah uses a combination of fluid-flow solvers and particle-based methods for solids, together with a novel asynchronous task-based approach with fully automated load balancing. Uintah demonstrates excellent weak and strong scalability at full machine capacity on XSEDE resources such as Ranger and Kraken, and through the use of a hybrid memory approach based on a combination of MPI and Pthreads, Uintah now runs on up to 262k cores on the DOE Jaguar system. In order to extend Uintah to heterogeneous systems, with ever-increasing CPU core counts and additional onnode GPUs, a new dynamic CPU-GPU task scheduler is designed and evaluated in this study. This new scheduler enables Uintah to fully exploit these architectures with support for asynchronous, outof- order scheduling of both CPU and GPU computational tasks. A new runtime system has also been implemented with an added multi-stage queuing architecture for efficient scheduling of CPU and GPU tasks. This new runtime system automatically handles the details of asynchronous memory copies to and from the GPU and introduces a novel method of pre-fetching and preparing GPU memory prior to GPU task execution. In this study this new design is examined in the context of a developing, hierarchical GPUbased ray tracing radiation transport model that provides Uintah with additional capabilities for heat transfer and electromagnetic wave propagation. The capabilities of this new scheduler design are tested by running at large scale on the modern heterogeneous systems, Keeneland and TitanDev, with up to 360 and 960 GPUs respectively. On these systems, we demonstrate significant speedups per GPU against a standard CPU core for our radiation problem.

Keywords: csafe, uintah



Scalable Large-scale Fluid-structure Interaction Solvers in the Uintah Framework via Hybrid Task-based Parallelism Algorithms
SCI Technical Report, Q. Meng, M. Berzins. No. UUSCI-2012-004, SCI Institute, University of Utah, 2012.

Uintah is a software framework that provides an environment for solving fluid-structure interaction problems on structured adaptive grids on large-scale science and engineering problems involving the solution of partial differential equations. Uintah uses a combination of fluid-flow solvers and particle-based methods for solids, together with adaptive meshing and a novel asynchronous task-based approach with fully automated load balancing. When applying Uintah to fluid-structure interaction problems with mesh refinement, the combination of adaptive meshing and the movement of structures through space present a formidable challenge in terms of achieving scalability on large-scale parallel computers. With core counts per socket continuing to grow along with the prospect of less memory per core, adopting a model that uses MPI to communicate between nodes and a shared memory model on-node is one approach to achieve scalability at full machine capacity on current and emerging large-scale systems. For this approach to be successful, it is necessary to design data-structures that large numbers of cores can simultaneously access without contention. These data structures and algorithms must also be designed to avoid the overhead involved with locks and other synchronization primitives when running on large number of cores per node, as contention for acquiring locks quickly becomes untenable. This scalability challenge is addressed here for Uintah, by the development of new hybrid runtime and scheduling algorithms combined with novel lockfree data structures, making it possible for Uintah to achieve excellent scalability for a challenging fluid-structure problem with mesh refinement on as many as 260K cores.

Keywords: uintah, csafe



Large Scale Parallel Solution of Incompressible Flow Problems using Uintah and hypre
SCI Technical Report, J. Schmidt, M. Berzins, J. Thornock, T. Saad, J. Sutherland. No. UUSCI-2012-002, SCI Institute, University of Utah, 2012.

The Uintah Software framework was developed to provide an environment for solving fluid-structure interaction problems on structured adaptive grids on large-scale, long-running, data-intensive problems. Uintah uses a combination of fluid-flow solvers and particle-based methods for solids together with a novel asynchronous task-based approach with fully automated load balancing. As Uintah is often used to solve compressible, low-Mach combustion applications, it is important to have a scalable linear solver. While there are many such solvers available, the scalability of those codes varies greatly. The hypre software offers a range of solvers and pre-conditioners for different types of grids. The weak scalability of Uintah and hypre is addressed for particular examples when applied to an incompressible flow problem relevant to combustion applications. After careful software engineering to reduce start-up costs, much better than expected weak scalability is seen for up to 100K cores on NSFs Kraken architecture and up to 200K+ cores, on DOEs new Titan machine.

Keywords: uintah, csafe



Biomedical Visual Computing: Case Studies and Challenges
C.R. Johnson. In IEEE Computing in Science and Engineering, Vol. 14, No. 1, pp. 12--21. 2012.
PubMed ID: 22545005
PubMed Central ID: PMC3336198

Computer simulation and visualization are having a substantial impact on biomedicine and other areas of science and engineering. Advanced simulation and data acquisition techniques allow biomedical researchers to investigate increasingly sophisticated biological function and structure. A continuing trend in all computational science and engineering applications is the increasing size of resulting datasets. This trend is also evident in data acquisition, especially in image acquisition in biology and medical image databases.

For example, in a collaboration between neuroscientist Robert Marc and our research team at the University of Utah's Scientific Computing and Imaging (SCI) Institute (www.sci.utah.edu), we're creating datasets of brain electron microscopy (EM) mosaics that are 16 terabytes in size. However, while there's no foreseeable end to the increase in our ability to produce simulation data or record observational data, our ability to use this data in meaningful ways is inhibited by current data analysis capabilities, which already lag far behind. Indeed, as the NIH-NSF Visualization Research Challenges report notes, to effectively understand and make use of the vast amounts of data researchers are producing is one of the greatest scientific challenges of the 21st century.

Visual data analysis involves creating images that convey salient information about underlying data and processes, enabling the detection and validation of expected results while leading to unexpected discoveries in science. This allows for the validation of new theoretical models, provides comparison between models and datasets, enables quantitative and qualitative querying, improves interpretation of data, and facilitates decision making. Scientists can use visual data analysis systems to explore \"what if\" scenarios, define hypotheses, and examine data under multiple perspectives and assumptions. In addition, they can identify connections between numerous attributes and quantitatively assess the reliability of hypotheses. In essence, visual data analysis is an integral part of scientific problem solving and discovery.

As applied to biomedical systems, visualization plays a crucial role in our ability to comprehend large and complex data-data that, in two, three, or more dimensions, convey insight into many diverse biomedical applications, including understanding neural connectivity within the brain, interpreting bioelectric currents within the heart, characterizing white-matter tracts by diffusion tensor imaging, and understanding morphology differences among different genetic mice phenotypes.

Keywords: kaust



Status of Release of the Uintah Computational Framework
SCI Technical Report, M. Berzins. No. UUSCI-2012-001, SCI Institute, University of Utah, 2012.

This report provides a summary of the status of the Uintah Computation Framework (UCF) software. Uintah is uniquely equipped to tackle large-scale multi-physics science and engineering problems on disparate length and time scales. The Uintah framework makes it possible to run adaptive computations on modern HPC architectures with tens and now hundreds of thousands of cores with complex communication/memory hierarchies. Uintah was orignally developed in the University of Utah Center for Simulation of Accidental Fires and Explosions (C-SAFE), a DOE-funded academic alliance project and then extended to the broader NSF snd DOE science and engineering communities. As Uintah is applicable to a wide range of engineering problems that involve fl uid-structure interactions with highly deformable structures it is used for a number of NSF-funded and DOE engineering projects. In this report the Uintah framework software is outlined and typical applications are illustrated. Uintah is open-source software that is available through the MIT open-source license at http://www.uintah.utah.edu/.



Fast, Effective BVH Updates for Animated Scenes
D. Kopta, T. Ize, J. Spjut, E. Brunvand, A. Davis, A. Kensler. In Proceedings of the Symposium on Interactive 3D Graphics and Games (I3D '12), pp. 197--204. 2012.
DOI: 10.1145/2159616.2159649

Bounding volume hierarchies (BVHs) are a popular acceleration structure choice for animated scenes rendered with ray tracing. This is due to the relative simplicity of refitting bounding volumes around moving geometry. However, the quality of such a refitted tree can degrade rapidly if objects in the scene deform or rearrange significantly as the animation progresses, resulting in dramatic increases in rendering times and a commensurate reduction in the frame rate. The BVH could be rebuilt on every frame, but this could take significant time. We present a method to efficiently extend refitting for animated scenes with tree rotations, a technique previously proposed for off-line improvement of BVH quality for static scenes. Tree rotations are local restructuring operations which can mitigate the effects that moving primitives have on BVH quality by rearranging nodes in the tree during each refit rather than triggering a full rebuild. The result is a fast, lightweight, incremental update algorithm that requires negligible memory, has minor update times, parallelizes easily, avoids significant degradation in tree quality or the need for rebuilding, and maintains fast rendering times. We show that our method approaches or exceeds the frame rates of other techniques and is consistently among the best options regardless of the animated scene.



Understanding Quasi-Periodic Fieldlines and Their Topology in Toroidal Magnetic Fields
A.R. Sanderson, G. Chen, X. Tricoche, E. Cohen. In Topological Methods in Data Analysis and Visualization II, Edited by R. Peikert and H. Carr and H. Hauser and R. Fuchs, Springer, pp. 125--140. 2012.
DOI: 10.1007/478-3-642-23175-9



Adaptive High-Order Discontinuous Galerkin Solution of Elastohydrodynamic Lubrication Point Contact Problems
H. Lu, M. Berzins, C.E. Goodyer, P.K. Jimack. In Advances in Engineering Software, Vol. 45, No. 1, pp. 313--324. 2012.
DOI: 10.1016/j.advengsoft.2011.10.006

This paper describes an adaptive implementation of a high order Discontinuous Galerkin (DG) method for the solution of elastohydrodynamic lubrication (EHL) point contact problems. These problems arise when modelling the thin lubricating film between contacts which are under sufficiently high pressure that the elastic deformation of the contacting elements cannot be neglected. The governing equations are highly nonlinear and include a second order partial differential equation that is derived via the thin-film approximation. Furthermore, the problem features a free boundary, which models where cavitation occurs, and this is automatically captured as part of the solution process. The need for spatial adaptivity stems from the highly variable length scales that are present in typical solutions. Results are presented which demonstrate both the effectiveness and the limitations of the proposed adaptive algorithm.

Keywords: Elastohydrodynamic lubrication, Discontinuous Galerkin, High polynomial degree, h-adaptivity, Nonlinear systems



DAG-Based Software Frameworks for PDEs
M. Berzins, Q. Meng, J. Schmidt, J.C. Sutherland. In Proceedings of Euro-Par 2011 Workshops, Part I, Lecture Notes in Computer Science (LNCS) 7155, Springer-Verlag Berlin Heidelberg, pp. 324--333. August, 2012.

The task-based approach to software and parallelism is well-known and has been proposed as a potential candidate, named the silver model, for exascale software. This approach is not yet widely used in the large-scale multi-core parallel computing of complex systems of partial differential equations. After surveying task-based approaches we investigate how well the Uintah software and an extension named Wasatch fit in the task-based paradigm and how well they perform on large scale parallel computers. The conclusion is that these approaches show great promise for petascale but that considerable algorithmic challenges remain.

Keywords: DOD, Uintah, CSAFE



An optimization framework for inversely estimating myocardial transmembrane potentials and localizing ischemia
D. Wang, R.M. Kirby, R.S. Macleod, C.R. Johnson. In Proceedings of the International Conference of the IEEE Engineering in Medicine and Biology Society (EMBS), pp. 1680--1683. 2011.
DOI: 10.1109/IEMBS.2011.6090483
PubMed ID: 22254648
PubMed Central ID: PMC3336368

By combining a static bidomain heart model with a torso conduction model, we studied the inverse electrocardiographic problem of computing the transmembrane potentials (TMPs) throughout the myocardium from a body-surface potential map, and then used the recovered potentials to localize myocardial ischemia. Our main contribution is solving the inverse problem within a constrained optimization framework, which is a generalization of previous methods for calculating transmembrane potentials. The framework offers ample flexibility for users to apply various physiologically-based constraints, and is well supported by mature algorithms and solvers developed by the optimization community. By avoiding the traditional inverse ECG approach of building the lead-field matrix, the framework greatly reduces computation cost and, by setting the associated forward problem as a constraint, the framework enables one to flexibly set individualized resolutions for each physical variable, a desirable feature for balancing model accuracy, ill-conditioning and computation tractability. Although the task of computing myocardial TMPs at an arbitrary time instance remains an open problem, we showed that it is possible to obtain TMPs with moderate accuracy during the ST segment by assuming all cardiac cells are at the plateau phase. Moreover, the calculated TMPs yielded a good estimate of ischemic regions, which was of more clinical interest than the voltage values themselves. We conducted finite element simulations of a phantom experiment over a 2D torso model with synthetic ischemic data. Preliminary results indicated that our approach is feasible and suitably accurate for the common case of transmural myocardial ischemia.



Cyber Science and Engineering: A Report of the National Science Foundation Advisory Committee for Cyberinfrastructure Task Force on Grand Challenges
J.T. Oden, O. Ghattas, J.L. King, B.I. Schneider, K. Bartschat, F. Darema, J. Drake, T. Dunning, D. Estep, S. Glotzer, M. Gurnis, C.R. Johnson, D.S. Katz, D. Keyes, S. Kiesler, S. Kim, J. Kinter, G. Klimeck, C.W. McCurdy, R. Moser, C. Ott, A. Patra, L. Petzold, T. Schlick, K. Schulten, V. Stodden, J. Tromp, M. Wheeler, S.J. Winter, C. Wu, K. Yelick. Note: NSF Report, 2011.

This document contains the findings and recommendations of the NSF – Advisory Committee for Cyberinfrastructure Task Force on Grand Challenges addressed by advances in Cyber Science and Engineering. The term Cyber Science and Engineering (CS&E) is introduced to describe the intellectual discipline that brings together core areas of science and engineering, computer science, and computational and applied mathematics in a concerted effort to use the cyberinfrastructure (CI) for scientific discovery and engineering innovations; CS&E is computational and data-based science and engineering enabled by CI. The report examines a host of broad issues faced in addressing the Grand Challenges of science and technology and explores how those can be met by advances in CI. Included in the report are recommendations for new programs and initiatives that will expand the portfolio of the Office of Cyberinfrastructure and that will be critical to advances in all areas of science and engineering that rely on the CI.



Advisory Committee for CyberInfrastructure Task Force on Software for Science and Engineering
D. Keyes, V. Taylor, T. Hey, S. Feldman, G. Allen, P. Colella, P. Cummings, F. Darema, J. Dongarra, T. Dunning, M. Ellisman, I. Foster, W. Gropp, C.R. Johnson, C. Kamath, R. Madduri, M. Mascagni, S.G. Parker, P. Raghavan, A. Trefethen, S. Valcourt, A. Patra, F. Choudhury, C. Cooper, P. McCartney, M. Parashar, T. Russell, B. Schneider, J. Schopf, N. Sharp. Note: NSF Report, 2011.

The Software for Science and Engineering (SSE) Task Force commenced in June 2009 with a charge that consisted of the following three elements:

Identify specific needs and opportunities across the spectrum of scientific software infrastructure. Characterize the specific needs and analyze technical gaps and opportunities for NSF to meet those needs through individual and systemic approaches. Design responsive approaches. Develop initiatives and programs led (or co-led) by NSF to grow, develop, and sustain the software infrastructure needed to support NSF’s mission of transformative research and innovation leading to scientific leadership and technological competitiveness. Address issues of institutional barriers. Anticipate, analyze and address both institutional and exogenous barriers to NSF’s promotion of such an infrastructure.

The SSE Task Force members participated in bi-weekly telecons to address the given charge. The telecons often included additional distinguished members of the scientific community beyond the task force membership engaged in software issues, as well as personnel from federal agencies outside of NSF who manage software programs. It was quickly acknowledged that a number of reports loosely and tightly related to SSE existed and should be leveraged. By September 2009, the task formed had formed three subcommittees focused on the following topics: (1) compute-intensive science, (2) data-intensive science, and (3) software evolution.



Sensitivity Analysis for the Optimization of Radiofrequency Ablation in the Presence of Material Parameter Uncertainty
I. Altrogge, T. Preusser, T. Kroeger, S. Haase, T. Paetz, R.M. Kirby. In International Journal for Uncertainty Quantification, 2011.

We present a sensitivity analysis of the optimization of the probe placement in radiofrequency (RF) ablation which takes the uncertainty associated with bio-physical tissue properties (electrical and thermal conductivity) into account. Our forward simulation of RF ablation is based upon a system of partial differential equations (PDEs) that describe the electric potential of the probe and the steady state of the induced heat. The probe placement is optimized by minimizing a temperature-based objective function such that the volume of destroyed tumor tissue is maximized. The resulting optimality system is solved with a multi-level gradient descent approach. By evaluating the corresponding optimality system for certain realizations of tissue parameters (i.e. at certain, well-chosen points in the stochastic space) the sensitivity of the system can be analyzed with respect to variations in the tissue parameters. For the interpolation in the stochastic space we use a stochastic finite element approach with piecewise multilinear ansatz functions on adaptively refined, hierarchical grids. We underscore the significance of the approach by applying the optimization to CT data obtained from a real RF ablation case.

Keywords: netl, stochastic sensitivity analysis, stochastic partial di erential equations, stochastic nite element method, adaptive sparse grid, heat transfer, multiscale modeling, representation of uncertainty



Implementation and Verification of a Nodally-Integrated Tetrahedral Element in FEBio
SCI Technical Report, S.A. Maas, B.J. Ellis, D.S. Rawlins, L.T. Edgar, C.R. Henak, J.A. Weiss. No. UUSCI-2011-007, SCI Institute, University of Utah, 2011.

Finite element simulations in computational biomechanics commonly require the discretization of extremely complicated geometries. Creating meshes for these complex geometries can be very difficult and time consuming using hexahedral elements. Automatic meshing algorithms exist for tetrahedral elements, but these elements often have numerical problems that discourage their use in complex finite element models. To overcome these problems we have implemented a stabilized, nodally-integrated tetrahedral element formulation in FEBio, our in-house developed finite element code, allowing researchers to use linear tetrahedral elements in their models and still obtain accurate solutions. In addition to facilitating automatic mesh generation, this also allows researchers to use mesh refinement algorithms which are fairly well developed for tetrahedral elements but not so much for hexahedral elements. In this document, the implementation of the stabilized, nodallyintegrated, tetrahedral element, named the \"UT4 element\", is described. Two slightly different variations of the nodally integrated tetrahedral element are considered. In one variation the entire virtual work is stabilized and in the other one the stabilization is only applied to the isochoric part of the virtual work. The implementation of both formulations has been verified and the convergence behavior illustrated using the patch test and three verification problems. Also, a model from our laboratory with very complex geometry is discretized and analyzed using the UT4 element to show its utility for a problem from the biomechanics literature. The convergence behavior of the UT4 element does vary depending on problem, tetrahedral mesh structure and choice of formulation parameters, but the results from the verification problems should assure analysts that a converged solution using the UT4 element can be obtained that is more accurate than the solution from a classical linear tetrahedral formulation.

Keywords: MRL



Dark Regions of No-Reflow on Late Gadolinium Enhancement Magnetic Resonance Imaging Result in Scar Formation After Atrial Fibrillation Ablation
C.J. McGann, E.G. Kholmovski, J.J. Blauer, S. Vijayakumar, T.S. Haslam, J.E. Cates, E.V. DiBella, N.S. Burgon, B. Wilson, A.J. Alexander, M.W. Prastawa, M. Daccarett, G. Vergara, N.W. Akoum, D.L. Parker, R.S. MacLeod, N.F. Marrouche. In Journal of the American College of Cardiology, Vol. 58, No. 2, pp. 177--185. 2011.
DOI: 10.1016/j.jacc.2011.04.008
PubMed ID: 21718914

Objectives: The aim of this study was to assess acute ablation injuries seen on late gadolinium enhancement (LGE) magnetic resonance imaging (MRI) immediately post-ablation (IPA) and the association with permanent scar 3 months post-ablation (3moPA).

Background: Success rates for atrial fibrillation catheter ablation vary significantly, in part because of limited information about the location, extent, and permanence of ablation injury at the time of procedure. Although the amount of scar on LGE MRI months after ablation correlates with procedure outcomes, early imaging predictors of scar remain elusive.

Methods: Thirty-seven patients presenting for atrial fibrillation ablation underwent high-resolution MRI with a 3-dimensional LGE sequence before ablation, IPA, and 3moPA using a 3-T scanner. The acute left atrial wall injuries on IPA scans were categorized as hyperenhancing (HE) or nonenhancing (NE) and compared with scar 3moPA.

Results: Heterogeneous injuries with HE and NE regions were identified in all patients. Dark NE regions in the left atrial wall on LGE MRI demonstrate findings similar to the \"no-reflow\" phenomenon. Although the left atrial wall showed similar amounts of HE, NE, and normal tissue IPA (37.7 ± 13\%, 34.3 ± 14\%, and 28.0 ± 11\%, respectively; p = NS), registration of IPA injuries with 3moPA scarring demonstrated that 59.0 ± 19\% of scar resulted from NE tissue, 30.6 ± 15\% from HE tissue, and 10.4 ± 5\% from tissue identified as normal. Paired t-test comparisons were all statistically significant among NE, HE, and normal tissue types (p less than 0.001). Arrhythmia recurrence at 1-year follow-up correlated with the degree of wall enhancement 3moPA (p = 0.02).

Conclusion: Radiofrequency ablation results in heterogeneous injury on LGE MRI with both HE and NE wall lesions. The NE lesions demonstrate no-reflow characteristics and reveal a better predictor of final scar at 3 months. Scar correlates with procedure outcomes, further highlighting the importance of early scar prediction. (J Am Coll Cardiol 2011;58:177–85) © 2011 by the American College of Cardiology Foundation



Smoothness-Increasing Accuracy-Conserving (SIAC) Postprocessing for Discontinuous Galerkin Solutions Over Structured Triangular Meshes
H. Mirzaee, Liangyue, J.K. Ryan, R.M. Kirby. In SIAM Journal of Numerical Analysis, Vol. 49, No. 5, pp. 1899--1920. 2011.

Theoretically and computationally, it is possible to demonstrate that the order of accuracy of a discontinuous Galerkin (DG) solution for linear hyperbolic equations can be improved from order k+1 to 2k+1 through the use of smoothness-increasing accuracy-conserving (SIAC) filtering. However, it is a computationally complex task to perform this in an efficient manner, which becomes an even greater issue considering nonquadrilateral mesh structures. In this paper, we present an extension of this SIAC filter to structured triangular meshes. The basic theoretical assumption in the previous implementations of the postprocessor limits the use to numerical solutions solved over a quadrilateral mesh. However, this assumption is restrictive, which in turn complicates the application of this postprocessing technique to general tessellations. Additionally, moving from quadrilateral meshes to triangulated ones introduces more complexity in the calculations as the number of integrations required increases. In this paper, we extend the current theoretical results to variable coefficient hyperbolic equations over structured triangular meshes and demonstrate the effectiveness of the application of this postprocessor to structured triangular meshes as well as exploring the effect of using inexact quadrature. We show that there is a direct theoretical extension to structured triangular meshes for hyperbolic equations with bounded variable coefficients. This is a challenging first step toward implementing SIAC filters for unstructured tessellations. We show that by using the usual B-spline implementation, we are able to improve on the order of accuracy as well as decrease the magnitude of the errors. These results are valid regardless of whether exact or inexact integration is used. The results here demonstrate that it is still possible, both theoretically and computationally, to improve to 2k+1 over the DG solution itself for structured triangular meshes.