We consider four asynchronous parallel algorithms for Implicit Monte Carlo (IMC) thermal radiation transport on spatially decomposed meshes. Two of the algorithms are from the production codes KULL from Lawrence Livermore National Laboratory and Milagro from Los Alamos National Laboratory. Improved versions of each of the existing algorithms are also presented. All algorithms were analyzed in an implementation of the KULL IMC package in ALEGRA, a Sandia National Laboratory high energy density physics code. The improved Milagro algorithm performed the best by scaling almost linearly out to 244 processors for well load balanced problems.
The success of Lagrangian contact modeling leads one to believe that important aspects of this capability may be used for multi-material modeling when only a portion of the simulation can be represented in a Lagrangian frame. We review current experience with two dual mesh technologies where one of these meshes is a Lagrangian mesh and the other is an Arbitrary Lagrangian/Eulerian (ALE) mesh. These methods are cast in the framework of an operator-split ALE algorithm where a Lagrangian step is followed by a remesh/remap step. An interface-coupled methodology is considered first. This technique is applicable to problems involving contact between materials of dissimilar compliance. The technique models the more compliant (soft) material as ALE while the less compliant (hard) material and associated interface are modeled in a Lagrangian fashion. Loads are transferred between the hard and soft materials via explicit transient dynamics contact algorithms. The use of these contact algorithms remove the requirement of node-tonode matching at the soft-hard interface. In the context of the operator-split ALE algorithm, a single Lagrangian step is performed using a mesh to mesh contact algorithm. At the end of the Lagrangian step the meshes will be slightly offset at the interface but non-interpenetrating. The ALE mesh nodes at the interface are then remeshed to their initial location relative to the Lagrangian body faces and the ALE mesh is smoothed, translated and rotated to follow Lagrangian body. Robust remeshing in the ALE region is required for success of this algorithm, and we describe current work in this area. The second method is an overlapping grid methodology that requires mapping of information between a Lagrangian mesh and an ALE mesh. The Lagrangian mesh describes a relatively hard body that interacts with softer material contained in the ALE mesh. A predicted solution for the velocity field is performed independently on both meshes. Element-centered velocity and momentum are transferred between the meshes using the volume transfer capability implemented in contact algorithms. Data from the ALE mesh is mapped to a phantom mesh that surrounds the Lagrangian mesh, providing for the reaction to the predicted motion of the Lagrangian material. Data from the Lagrangian mesh is mapped directly to the ALE mesh. A momentum balance is performed on both meshes to adjust the velocity field to account for the interaction of the material from the other mesh. Subsequent, remeshing and remapping of the ALE mesh is performed to allow large deformation of the softer material. We overview current progress using this approach and discuss avenues for future research and development.
Study of the triggered plasma opening switch (TPOS) characteristics is in progress via an ion current collection diagnostic (ICCD), in addition to offline apparatus. This initial ion current collection diagnostic has been designed, fabricated, and tested on the TPOS in order to explore the opening profile of the main switch. The initial ion current collection device utilizes five collectors which are positioned perpendicularly to the main switch stage in order to collect radially traveling ions. It has been shown through analytical prowess that this specific geometry can be treated as a planar case of the Child-Langmuir law with only a 6% deviation from the cylindrical case. Additionally, magnetostatic simulations with self consistent space charge emitting surfaces of the main switch using the Trak code are under way. It is hoped that the simulations will provide evidence in support of both the analytical derivations and experimental data. Finally, an improved design of the ICCD (containing 12 collectors in the axial direction) is presently being implemented.
We provide a common framework for compatible discretizations using algebraic topology to guide our analysis. The main concept is the natural inner product on cochains, which induces a combinatorial Hodge theory. The framework comprises of mutually consistent operations of differentiation and integration, has a discrete Stokes theorem, and preserves the invariants of the DeRham cohomology groups. The latter allows for an elementary calculation of the kernel of the discrete Laplacian. Our framework provides an abstraction that includes examples of compatible finite element, finite volume and finite difference methods. We describe how these methods result from the choice of a reconstruction operator and when they are equivalent.
The overlap of computation and communication has long been considered to be a significant performance benefit for applications. Similarly, the ability of the Message Passing Interface (MPI) to make independent progress (that is, to make progress on outstanding communication operations while not in the MPI library) is also believed to yield performance benefits. Using an intelligent network interface to offload the work required to support overlap and independent progress is thought to be an ideal solution, but the benefits of this approach have not been studied in depth at the application level. This lack of analysis is complicated by the fact that most MPI implementations do not sufficiently support overlap or independent progress. Recent work has demonstrated a quantifiable advantage for an MPI implementation that uses offload to provide overlap and independent progress. The study is conducted on two different platforms with each having two MPI implementations (one with and one without independent progress). Thus, identical network hardware and virtually identical software stacks are used. Furthermore, one platform, ASCI Red, allows further separation of features such as overlap and offload. Thus, this paper extends previous work by further qualifying the source of the performance advantage: offload, overlap, or independent progress.
Over the last decade and a half, tabu search algorithms for machine scheduling have gained a near-mythical reputation by consistently equaling or establishing state-of-the-art performance levels on a range of academic and real-world problems. Yet, despite these successes, remarkably little research has been devoted to developing an understanding of why tabu search is so effective on this problem class. In this paper, we report results that provide significant progress in this direction. We consider Nowicki and Smutnicki's i-TSAB tabu search algorithm, which represents the current state-of-the-art for the makespan-minimization form of the classical jobshop scheduling problem. Via a series of controlled experiments, we identify those components of i-TSAB that enable it to achieve state-of-the-art performance levels. In doing so, we expose a number of misconceptions regarding the behavior and/or benefits of tabu search and other local search metaheuristics for the job-shop problem. Our results also serve to focus future research, by identifying those specific directions that are most likely to yield further improvements in performance.
In this paper, we analyze the relationship between pool maintenance schemes, long-term memory mechanisms, and search space structure, with the goal of placing metaheuristic design on a more concrete foundation.
High-power Z pinches on Sandia National Laboratories Z facility can be used in a variety of experiments to radiatively heat samples placed some distance away from the Z-pinch plasma. In such experiments, the heating radiation spectrum is influenced by both the Z-pinch emission and the re-emission of radiation from the high-Z surfaces that make up the Z-pinch diode. To test the understanding of the amplitude and spectral distribution of the heating radiation, thin foils containing both Al and MgF{sub 2} were heated by a 100-130 TW Z pinch. The heating of these samples was studied through the ionization distribution in each material as measured by x-ray absorption spectra. The resulting plasma conditions are inferred from a least-squares comparison between the measured spectra and calculations of the Al and Mg 1s {yields} 2p absorption over a large range of temperatures and densities. These plasma conditions are then compared to radiation-hydrodynamics simulations of the sample dynamics and are found to agree within 1{sigma} to the best-fit conditions. This agreement indicates that both the driving radiation spectrum and the heating of the Al and MgF{sub 2} samples is understood within the accuracy of the spectroscopic method.
The mission of Radiographic Integrated Test Stand-6 (RITS-6) facility is to provide the underlying science and technology for pulsed-power-driven flash radiographic X-ray sources for the National Nuclear Security Administration (NNSA). Flash X-ray radiography is a penetrating diagnostic to discern the internal structure in dynamic experiments. Short (~50 nanosecond (ns) duration) bursts of very high intensity X-rays from mm-scale source sizes are required at a variety of voltages to address this mission. RITS-6 was designed and is used to both develop the accelerator technology needed for these experiments and serves as the principal test stand to develop the high intensity electron beam diodes that generate the required X-ray sources. RITS is currently in operation with three induction cavities (RITS-3) with a maximum voltage output of 5.5 MV and is classified as a low hazard non-nuclear facility in accordance with CPR 400.1.1, Chapter 13, Hazards Identification/Analysis and Risk Management. The facility will be expanded from three to six cavities (RITS-6) effectively doubling the operating voltage. The increase in the operating voltage to above 10 MV has resulted in RITS-6 being classified as an accelerator facility. RITS-6 will come under DOE Order 420.2B, Safety of Accelerator Facilities. The hazards of RITS are detailed in the "Safety Assessment Document for the Radiographic Integrated Test Stand Facility." The principal non-industrial hazard is prompt x-ray radiation. As the operating voltage is increased, both the penetration power and the total amount (dose) of x-rays are increased, thereby increasing the risk to local personnel. Fixed site shielding (predominantly concrete walls and a steel/lead skyshine shield) is used to attenuate these x-rays and mitigate this risk. This SAND Report details the anticipated x-ray doses, the shielding design, and the anticipated x-ray doses external to this shielding structure both in areas where administrative access control restricts occupation and in adjacent uncontrolled areas.
The reinforced carbon-carbon (RCC) heat shield components on the Space Shuttle's wings must withstand harsh atmospheric reentry environments where the wing leading edge can reach temperatures of 3,000 F. Potential damage includes impact damage, micro cracks, oxidation in the silicon carbide-to-carbon-carbon layers, and interlaminar disbonds. Since accumulated damage in the thick, carbon-carbon and silicon-carbide layers of the heat shields can lead to catastrophic failure of the Shuttle's heat protection system, it was essential for NASA to institute an accurate health monitoring program. NASA's goal was to obtain turnkey inspection systems that could certify the integrity of the Shuttle heat shields prior to each mission. Because of the possibility of damaging the heat shields during removal, the NDI devices must be deployed without removing the leading edge panels from the wing. Recently, NASA selected a multi-method approach for inspecting the wing leading edge which includes eddy current, thermography, and ultrasonics. The complementary superposition of these three inspection techniques produces a rigorous Orbiter certification process that can reliably detect the array of flaws expected in the Shuttle's heat shields. Sandia Labs produced an in-situ ultrasonic inspection method while NASA Langley developed the eddy current and thermographic techniques. An extensive validation process, including blind inspections monitored by NASA officials, demonstrated the ability of these inspection systems to meet the accuracy, sensitivity, and reliability requirements. This report presents the ultrasonic NDI development process and the final hardware configuration. The work included the use of flight hardware and scrap heat shield panels to discover and overcome the obstacles associated with damage detection in the RCC material. Optimum combinations of custom ultrasonic probes and data analyses were merged with the inspection procedures needed to properly survey the heat shield panels. System features were introduced to minimize the potential for human factors errors in identifying and locating the flaws. The in-situ NDI team completed the transfer of this technology to NASA and USA employees so that they can complete 'Return-to-Flight' certification inspections on all Shuttle Orbiters prior to each launch.
Molecular-dynamics simulations are used to sample the single-chain form factor of labelled sub-chains in model polymer networks under elongational strain. We observe very similar results for randomly cross-linked and for randomly end-linked networks with the same average strand length and see no indication of lozenge-like scattering patterns reported for some experimental systems. Our data analysis shows that a recent variant of the tube model quantitatively describes scattering in the Guinier regime as well as the macroscopic elastic properties. The observed failure of the theory outside the Guinier regime is shown to be due to non-Gaussian pair-distance distributions.
Numerous technologies including solid-state lighting, displays, and traffic signals can benefit from efficient, color-selectable light sources that are driven electrically. Semiconductor nanocrystals are attractive types of chromophores that combine size-controlled emission colors and high emission efficiencies with excellent photostability and chemical flexibility. Applications of nanocrystals in light-emitting technologies, however, have been significantly hindered by difficulties in achieving direct electrical injection of carriers. Here we report the first successful demonstration of electroluminescence from an all-inorganic, nanocrystal-based architecture in which semiconductor nanocrystals are incorporated into a p-n junction formed from GaN injection layers. The critical step in the fabrication of these nanocrystal/GaN hybrid structures is the use of a novel deposition technique, energetic neutral atom beam lithography/epitaxy, that allows for the encapsulation of nanocrystals within a GaN matrix without adversely affecting either the nanocrystal integrity or its luminescence properties. We demonstrate electroluminescence (injection efficiencies of at least 1%) in both single- and two-color regimes using structures comprising either a single monolayer or a bilayer of nanocrystals.
Large-scale three dimensional molecular dynamics simulations of hopper flow are presented. The flow rate of the system is controlled by the width of the aperture at the bottom. As the steady-state flow rate is reduced, the force distribution P(f) changes only slightly, while there is a large change in the impulse distribution P(i). In both cases, the distributions show an increase in small forces or impulses as the systems approach jamming, the opposite of that seen in previous Lennard-Jones simulations. This occurs dynamically as well for a hopper that transitions from a flowing to a jammed state over time. The final jammed P(f) is quite distinct from a poured packing P(f) in the same geometry. The change in P(i) is a much stronger indicator of the approach to jamming. The formation of a peak or plateau in P(f) at the average force is not a general feature of the approach to jamming.
Polysilane materials exhibit large photo-induced refractive index changes under low incident optical fluences, making them attractive candidates for applications in which rapid patterning of photonic device structures is desired immediately prior to their use. This agile fabrication strategy for integrated photonics inherently requires that optical exposure, and associated material response, occurs in nonlaboratory environments, motivating the study of environmental conditions on the photoinduced response of the material. The present work examines the impact of atmosphere on the photosensitive response of poly(methylphenylsilane) (PMPS) thin films in terms of both photoinduced absorption change and refractive index modification. Material was subjected to UV light exposure resonant with the lowest energy optical transition associated with the conjugated Si-Si backbone. Exposures were performed in both aerobic and anaerobic atmospheres (oxygen, air, nitrogen, and 5% H{sub 2}/95% N{sub 2}). The results clearly demonstrate that the photosensitive response of this model polysilane material was dramatically affected by local environment, exhibiting a photoinduced refractive index change, when exposed under an oxygen containing atmosphere, that was twice that observed under anaerobic conditions. This effect is discussed in terms of photo-oxidation processes within the polysilane structure and in the context of the need for predictable photosensitive refractive index change in varied photoimprinting environments.
A novel dual stage chemiluminescence detection system incorporating individually controlled hot stages has been developed and applied to probe for material interaction effects during polymer degradation. Utilization of this system has resulted in experimental confirmation for the first time that in an oxidizing environment a degrading polymer A (in this case polypropylene, PP) is capable of infecting a different polymer B (in this case polybutadiene, HTPB) over a relatively large distance. In the presence of the infectious degrading polymer A, the thermal degradation of polymer B is observed over a significantly shorter time period. Consistent with infectious volatiles from material A initiating the degradation process in material B it was demonstrated that traces (micrograms) of a thermally sensitive peroxide in the vicinity of PP could induce degradation remotely. This observation documents cross-infectious phenomena between different polymers and has major consequences for polymer interactions, understanding fundamental degradation processes and long-term aging effects under combined material exposures.
COBIT is a set of documents that provides guidance for computer security. This report introduces COBIT by answering the following questions, after first defining acronyms and presenting definitions: 1. Why is COBIT valuable? 2. What is COBIT?, and 3. What documents are related to COBIT? (The answer to the last question constitutes the bulk of this report.) This report also provides more detailed review of three documents. The first two documents--COBIT Security Baseline{trademark} and COBIT Quickstart{trademark}--are initial documents, designed to get people started. The third document-Control Practices-is a ''final'' document, so to speak, designed to take people all the way down into the details. Control Practices is the detail.
Sandia National Laboratories Z Refurbishment (ZR) Project formally began in August 2002 to increase the Z Accelerator's utilization by providing the capability to perform more shots, improve precision and pulse shape variability, increase delivered current, and accomplish the improvements with minimal disruption to Z's ongoing programs. A project overview was provided at the 14th International Pulsed Power Conference in 2003. This paper provides an update of the project including architectural changes over the past two years, timeframe for completion, and overall design and fabrication status.
The Mg-Li-N-H system is a very promising hydrogen storage material due to its high capacity, reversibility and moderate operating conditions. Some of thermodynamic and structural properties for this system are characterized here. Pressure-composition isotherms are measured and presented in this paper for absorption-desorption at 220, 200 and 180 C. Powder X-ray diffraction (XRD) and Fourier Transform Infrared (FTIR) analysis were carried out for samples at various degrees of hydrogenation. These results provide information about the structural changes during absorption/desorption. The mixture of (2LiNH{sub 2} + MgH{sub 2}) partially converts to (Mg(NH{sub 2}){sub 2} + 2LiH) when heated at 220 C and 100 bar of hydrogen without undergoing desorption. Based on two distinct parts which appear in all of the pressure-composition isotherms (180-220 C), two reactions taking place isothermally in hydrogen absorption/desorption are proposed for the material starting with (2LiNH{sub 2} + MgH{sub 2}) or (Mg(NH{sub 2}){sub 2} + 2LiH). These reactions include a single solid-phase reaction, corresponding to the sloping region for hydrogen weight percent (Hwt%) smaller than 1.5%, and a multiple-phase reaction, corresponding to a plateau region for Hwt.% > 1.5 in the isotherms. During hydrogen absorption/desorption, the single-solid-phase reaction corresponds to the forming/consuming of NH{sub 2} which is bonded to Li and the multiple-solid-phase reaction corresponds to forming/consuming Mg(NH{sub 2}){sub 2} and LiH. A mechanism for the sorption reactions has been proposed.
The in vivo bone response of 3D periodic hydroxyapatite (HA) scaffolds is investigated. Two groups of HA scaffolds (11 mm diameter x 3.5 mm thick) are fabricated by direct-write assembly of a concentrated HA ink. The scaffolds consist of cylindrical rods periodically arranged into four quadrants with varying separation distances between rods. In the first group, HA rods (250 {micro}m in diameter) are patterned to create pore channels, whose areal dimensions are 250 x 250 {micro}m{sup 2} in quadrant 1, 250 x 500 {micro}m{sup 2} in quadrants 2 and 4, and 500 x 500 {micro}m{sup 2} in quadrant 3. In the second group, HA rods (400 {micro}m in diameter) are patterned to create pore channels, whose areal dimensions of 500 x 500 {micro}m{sup 2} in quadrant 1, 500 x 750 {micro}m{sup 2} in quadrants 2 and 4, and 750 x 750 {micro}m{sup 2} in quadrant 3. Each group of scaffolds is partially densified by sintering at 1200 C prior to being implanted bilaterally in trephine defects of skeletally mature New Zealand White rabbits. Their tissue response is evaluated at 8 and 16 weeks using micro-computed tomography, histology, and scanning electron microscopy. New trabecular bone is conducted rapidly and efficiently across substantial distances within these patterned 3D HA scaffolds. Our observations suggest that HA rods are first coated with a layer of new bone followed by subsequent scaffold infilling via outward and inward radial growth of the coated regions. Direct-write assembly of 3D periodic scaffolds composed of micro-porous HA rods arrayed to produce macro-pores that are size-matched to trabecular bone may represent an optimal strategy for bone repair and replacement structures.
We derive here the form for the exact exchange energy density for a density that decays with Gaussian-type behavior at long range. This functional is intermediate between the B88 and the PW91 exchange functionals. Using this modified functional to match the form expected for Gaussian densities, we propose the X3LYP extended functional. We find that X3LYP significantly outperforms Becke three parameter Lee-Yang-Parr (B3LYP) for describing van der Waals and hydrogen bond interactions, while performing slightly better than B3LYP for predicting heats of formation, ionization potentials, electron affinities, proton affinities, and total atomic energies as validated with the extended G2 set of atoms and molecules. Thus X3LYP greatly enlarges the field of applications for density functional theory. In particular the success of X3LYP in describing the water dimer (with Re and De within the error bars of the most accurate determinations) makes it an excellent candidate for predicting accurate ligand-protein and ligand-DNA interactions.
Molecular compounds-comprised of mechanically interlocked components-such as rotaxanes and catenanes can be designed to display readily controllable internal movements of one component with respect to the other. Since theweak noncovalent bonding interactions that contribute to the template-directed synthesis of such compounds live on between the components thereafter, they can be activated such that the components move in either a linear fashion (rotaxanes) or a rotary manner (catenanes). These molecules can be activated by switching the recognition elements off and on between components chemically, electrically, or optically, such that they perform motions reminiscent of the moving parts in macroscopic machines. This review will highlight how the emergence ofthe mechanical bond in chemistry during the last two decades has brought with it a real prospect of integrating a bottom-up approach, based on molecular design and micro- and nanofabrication, to construct molecular electronic devices that store information at very high densities using minimal power. Although most of the research reported in this review on switchable catenanes and rotaxanes has been carried out in the context of solution-phase mechanical processes, recent results demonstrate that relative mechanical movements between the components in interlocked molecules can be stimulated (a) chemically in Langmuir and Langmuir-Blodgett films, (b) electrochemically as self-assembled monolayers on gold, and (c) electronically within the settings of solid-state devices. Not only has reversible, electronically driven switching been observed in devices incorporating a bistable [2]catenane, but a crosspoint random access memory circuit has been fabricated using an amphiphilic, bistable [2]rotaxane. The experiments provide strong evidence that switchable catenanes and rotaxanes operate mechanically in a soft-matter environment and can withstand simple device-processing steps. Studies on single-walled carbon nanotubes used as one of the electrodes in molecular switch tunnel junctions have revealed that interfacial chemical interactions involving electrodes containing carbon, silicon, and oxygen are good choices when carrying out molecular electronics on the class of rotaxane- and catenane-based molecules reported in this review. This conclusion is supported by differential conductance measurements (at 4K) made with single-molecule transistors using the break-junction method. It transpires that the electronic transport properties in such devices are more sensitive to the chemical nature of the molecule-electrode contacts than the details of the molecules' electronic structure away from the contacts. This result has profound implications for molecular electronics and highlights the importance of also considering the molecules and the electrodes as an integrated system. It all adds up to an integrated systems-oriented approach to nanotechnology that finds its inspiration in the transfer of concepts like molecular recognition from the life sciences into materials science and provides a model for how, in principle, to transfer elements of traditional chemistry to technology platforms that are being developed on the nanoscale. Before there can be any serious prospect of a technology, there has to be some good, sound science in the making. Molecular electronics is very much in its infancy and, as such, it can be expected to give rise to a great deal of intellectually stimulating science before it stands half a chance of becoming a viable companion to silicon-based technology.
We use the density functional theory and x-ray and neutron diffraction to investigate the crystal structures and reaction mechanisms of intermediate phases likely to be involved in decomposition of the potential hydrogen storage material LiAlH{sub 4}. First, we explore the decomposition mechanism of monoclinic LiAlH4 into monoclinic Li{sub 3}AlH{sub 6} plus face-centered cubic (fcc) Al and hydrogen. We find that this reaction proceeds through a five-step mechanism with an overall activation barrier of 36.9 kcal/mol. The simulated x ray and neutron diffraction patterns from LiAlH{sub 4} and Li{sub 3}AlH{sub 6} agree well with experimental data. On the other hand, the alternative decomposition of LiAlH{sub 4} into LiAlH2 plus H2 is predicted to be unstable with respect to that through Li{sub 3}AlH{sub 6}. Next, we investigate thermal decomposition of Li{sub 3}AlH{sub 6} into fcc LiH plus Al and hydrogen, occurring through a four-step mechanism with an activation barrier of 17.4 kcal/mol for the rate-limiting step. In the first and second steps, two Li atoms accept two H atoms from AlH{sub 6} to form the stable Li-H-Li-H complex. Then, two sequential H2 desorption steps are followed, which eventually result in fcc LiH plus fcc Al and hydrogen: Li{sub 3}AlH{sub 6}(monoclinic) {yields} 3 LiH(fcc) + Al(fcc) + 3/2 H{sub 2} is endothermic by 15.8 kcal/mol. The dissociation energy of 15.8 kcal/mol per formula unit compares to experimental enthalpies in the range of 9.8-23.9 kcal/mol. Finally, we explore thermal decomposition of LiH, LiH(s) + Al(s) {yields} LiAl(s) + 1/2 H{sub 2}(g) is endothermic by 4.6 kcal/mol. The B32 phase, which we predict as the lowest energy structure for LiAl, shows covalent bond characters in the Al-Al direction. Additionally, we determine that transformation of LiH plus Al into LiAlH is unstable with respect to transformation of LiH through LiAl.
Molecular dynamics calculations are performed to study the effect of deformation sequence and history on the inelastic behavior of copper interfaces on the nanoscale. An asymmetric 45 deg tilt bicrystal interface is examined, representing an idealized high-angle grain boundary interface. The interface model is subjected to three different deformation paths: tension then shear, shear then tension, and combined proportional tension and shear. Analysis shows that path-history dependent material behavior is confined within a finite layer of deformation around the bicrystal interface. The relationships between length scale and interface properties, such as the thickness of the path-history dependent layer and the interface strength, are discussed in detail.
A conforming representation composed of 2D finite elements and finite Fourier series is applied to 3D nonlinear non-ideal magnetohydrodynamics using a semi-implicit time-advance. The self-adjoint semi-implicit operator and variational approach to spatial discretization are synergistic and enable simulation in the extremely stiff conditions found in high temperature plasmas without sacrificing the geometric flexibility needed for modeling laboratory experiments. Growth rates for resistive tearing modes with experimentally relevant Lundquist number are computed accurately with time-steps that are large with respect to the global Alfven time and moderate spatial resolution when the finite elements have basis functions of polynomial degree (p) two or larger. An error diffusion method controls the generation of magnetic divergence error. Convergence studies show that this approach is effective for continuous basis functions with p {ge} 2, where the number of test functions for the divergence control terms is less than the number of degrees of freedom in the expansion for vector fields. Anisotropic thermal conduction at realistic ratios of parallel to perpendicular conductivity (x{parallel}/x{perpendicular}) is computed accurately with p {ge} 3 without mesh alignment. A simulation of tearing-mode evolution for a shaped toroidal tokamak equilibrium demonstrates the effectiveness of the algorithm in nonlinear conditions, and its results are used to verify the accuracy of the numerical anisotropic thermal conduction in 3D magnetic topologies.