Qubit-ADAPT-VQE: An Adaptive Algorithm for Constructing Hardware-Efficient Ansätze on a Quantum Processor
Not Available
Tang, Ho Lun (ORCID:0000000268757195)↗
SEARCH · Search NASA
Results for “Adaptivity”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Adaptive Data Rate Techniques for Energy Constrained Ad Hoc LoRa Networks.
Abstract not provided.
Heeger, Derek↗
Electronic Scanning Strategies in Adaptive Electrical Capacitance Volume Tomography: Tradeoffs and Prospects
Electrical Capacitance Volume Tomography (ECVT) has been applied for imaging of multiphase flows found in industrial applications. The ill-posed nature of the image reconstruction problem in ECVT and the consequent low resolution can be alleviated by employing electronic scanning enabled by electrode segmentation and reconfiguration during data acquisition. Here we study electronic scanning strategies that mimic physical rotation and shifting of the sensor along its symmetry axis. First, we study the feasibility of electronic scanning by analyzing the capacitance transducer circuit in SPICE. Then, we simulate electronic scanning using the finite element method for different electrode shapes, for which we compare the image reconstruction results and acquisition time. We find a noticeable improvement in image resolution for the scanning cases over conventional ECVT. Lastly, among the scanning cases, we emphasize a particular electrode shape that provides the best image resolution along with the minimal amount of acquisition time.
47 OTHER INSTRUMENTATION↗
Demographic Microsimulator for Integrated Urban Systems: Adapting Panel Survey of Income Dynamics to Capture the Continuum of Life
Agent-based models (ABMs) in transportation modeling simulate activity and travel decisions at the disaggregate level of households and individuals. To do this, ABMs require detailed and realistic information on agents’ socioeconomic and demographic characteristics. Various synthetic population generators have been proposed to address this need. However, most of those currently in practice are cross-sectional in nature and do not account for the dynamics within households and individuals as they progress through life events over time. This is a major shortcoming, as literature has shown that transportation decisions are affected by the transition between and co-occurrence of life cycle events. While some demographic evolution simulators have been proposed to address this issue, they are developed using cross-sectional data and capture only a small set of life cycle events and their interdependence. Addressing these drawbacks, we propose a demographic microsimulator (DEMOS) that captures the “continuum of life” by considering a range of household- and individual-level life cycle events. DEMOS is developed using the Panel Survey of Income Dynamics, one of the world’s longest-running longitudinal surveys. The DEMOS submodels consider key life cycle events that are influenced by agents’ demographic variables. DEMOS is applied to evolve the population of the San Francisco Bay Area over a 9-year horizon. Results demonstrate how DEMOS generates life trajectories and how DEMOS outputs match the observed demographic trends. DEMOS is expected to enable longitudinal analysis in the context of ABMs and expand ABMs analyses relating to dynamic processes such as household-level vehicle transactions.
Demographic evolution↗
Thermal Adaptation of Enzyme‐Mediated Processes Reduces Simulated Soil CO2 Fluxes Upon Soil Warming
Abstract Understanding factors influencing carbon effluxes from soils to the atmosphere is important in a world experiencing climatic change. Two important uncertainties related to soil organic carbon (SOC) stock responses to a changing climate are (a) whether soil microbial communities acclimate or adapt to changes in soil temperature and (b) how to represent this process in SOC models. To further explore these issues, we included thermal adaptation of enzyme‐mediated processes in a mechanistic SOC model (ReSOM) using the macromolecular rate theory. Thermal adaptation is defined here to encompass all potential responses of soil microbes and microbial communities following a change in temperature. To assess the effects of thermal adaptation of enzyme‐mediated processes on simulated SOC losses, ReSOM was applied to data collected from a 13‐year soil warming experiment. Results show that a model omitting thermal adaptation of enzyme‐mediated processes substantially overestimates observed CO 2 effluxes during the initial years of soil warming. The bias against observed CO 2 effluxes was lower for models including thermal adaptation of enzyme‐mediated processes. In addition, for a simulated linear 3°C soil warming over 100 years, models including thermal adaptation of enzyme‐mediated processes simulated SOC losses of a factor of three smaller than models omitting this process. As thermal adaptation of microbial community characteristics is generally not included in models simulating feedback between the soil, biosphere and atmosphere, we encourage future studies to assess the potential impact that microbial adaptation has on soil carbon – climate feedback representations in models. Plain Language Summary A major uncertainty in projecting how much soil organic carbon (SOC) will be converted to CO 2 as a consequence of climate change is related to how soil microbes may adapt to increasing soil temperatures. While this “microbial thermal adaptation” has been shown to occur in short‐term lab incubation experiments, its effect on SOC cycling on a decadal timescale is not clear. To address this knowledge gap, a mechanistic SOC model was used to simulate data collected from a 13‐year soil warming experiment, to assess how microbial thermal adaptation affects predicted SOC losses upon soil warming. The model results show that incorporating microbial thermal adaptation into the model led to reduced CO 2 effluxes from the soil to the atmosphere compared to the common approach of omitting this mechanism. Our results imply that projected SOC losses for the decades to come may be reduced when this mechanism is incorporated in land models. We therefore advocate for more research on the mechanisms controlling microbial thermal adaptation, and how to implement this mechanism in SOC models. Key Points A crucial aspect of soil organic carbon (SOC) models is the representation of soil microbes Predicted soil CO 2 fluxes upon soil warming are reduced when accounting for microbial thermal adaptation On a centennial time scale, this thermal adaptation results in up to a factor of three lower predicted SOC loss
Van de Broek, Marijn↗
A global assessment of policy tools to support climate adaptation
Governments, businesses, and civil society organizations have diverse policy tools to incentivize adaptation. Policy tools can shape the type and extent of adaptation, and therefore, function either as barriers or enablers for reducing risk and vulnerability. Using data from a systematic review of academic literature on global adaptation responses to climate change (n = 1549 peer-reviewed articles), we categorize the types of policy tools used to shape climate adaptation. We apply qualitative and quantitative analyses to assess the contexts where particular tools are used, along with equity implications for groups targeted by the tools, and the tools’ relationships with transformational adaptation indicators such as the depth, scope, and speed of adaptation. We find diverse types of tools documented across sectors and geographic regions. We also identify a mismatch between the tools that consider equity and those that yield more transformational adaptations. Direct regulations, plans, and capacity building are associated with higher depth and scope of adaptation (thus transformational adaptation), while economic instruments, information provisioning, and networks are not; the latter tools, however, are more likely to target marginalized groups in their design and implementation. We identify multiple research gaps, including a need to assess instrument mixes rather than single tools and to assess adaptations that result from policy implementation. Key policy insights Information-based approaches, networks, and economic instruments are the most frequently documented adaptation policy tools worldwide. Direct regulations, plans, and capacity building are associated with higher depth and scope of adaptation, and thus more transformational adaptation. Capacity building, economic instruments, networks, and information provisioning approaches are more likely to target specific marginalized groups and thus equity challenges. There are many regions and sectors where certain tools are not widely documented (e.g. regulations and plans in Africa and Asia), representing a key research gap.
54 ENVIRONMENTAL SCIENCES↗
Adaptation Strategies Strongly Reduce the Future Impacts of Climate Change on Simulated Crop Yields
Abstract Simulations of crop yield due to climate change vary widely between models, locations, species, management strategies, and Representative Concentration Pathways (RCPs). To understand how climate and adaptation affects yield change, we developed a meta‐model based on 8703 site‐level process‐model simulations of yield with different future adaptation strategies and climate scenarios for maize, rice, wheat and soybean. We tested 10 statistical models, including some machine learning models, to predict the percentage change in projected future yield relative to the baseline period (2000–2010) as a function of explanatory variables related to adaptation strategy and climate change. We used the best model to produce global maps of yield change for the RCP4.5 scenario and identify the most influential variables affecting yield change using Shapley additive explanations. For most locations, adaptation was the most influential factor determining the projected yield change for maize, rice and wheat. Without adaptation under RCP4.5, all crops are expected to experience average global yield losses of 6%–21%. Adaptation alleviates this average projected loss by 1–13 percentage points. Maize was most responsive to adaptive practices with a projected mean yield loss of −21% [range across locations: −63%, +3.7%] without adaptation and −7.5% [range: −46%, +13%] with adaptation. For maize and rice, irrigation method and cultivar choice were the adaptation types predicted to most prevent large yield losses, respectively. When adaptation practices are applied, some areas are predicted to experience yield gains, especially at northern high latitudes. These results reveal the critical importance of implementing adequate adaptation strategies to mitigate the impact of climate change on crop yields.
54 ENVIRONMENTAL SCIENCES↗
Recommended Actions to Improve Adapter Safety
With the rapid advancement and acceleration in the electric vehicle (EV) industry within the United States, major automakers and EV charging companies are increasingly adopting the North American Charging Standard (NACS) connector style, now officially known as J3400. This shift is expected to enhance charging infrastructure, providing a better customer experience by making it easier for all EV drivers to access a wider network of direct-current (DC) fast chargers (DCFCs). However, the adoption of the J3400 standard presents challenges for many EVs already on the roads and some currently coming off production lines that are equipped with the Combined Charging System (CCS) connector, which this report will refer to as the North American standard, CCS1. These vehicles will need adapters to use new or existing J3400 infrastructure. During this transition, several issues have emerged. Firstly, there is a need to standardize the new connector type to ensure it is interoperable, safe, and reliable. Second, existing CCS EV drivers need a way to access the J3400 network, which will require electric vehicle supply equipment (EVSE) or sites with both connector types, driver-provided adapters to physically convert from CCS to J3400, or EVSE with retained adapters designed for use with the EVSE. Third, adapter standards will need to be written to specify how they will be designed and what evaluations will be needed to ensure safe and reliable performance. To address these challenges, adapters that support different types of charging connectors will be essential. These adapters will play a crucial role in supporting the transition and ensuring continued service for legacy EVs with CCS inlets as the J3400 standard becomes the predominant one in the United States. Consequently, the National Charging Experience (ChargeX) Consortium has investigated and performed a teardown analysis on the different adapter versions on the market. The aim is to create a failure mode and effects analysis (FMEA) on what are expected to be the most common adapter types used in this transition. In order to support this work, we executed an FMEA exercise with the main goal of identifying gaps in the existing adapters' performance and conformance to the most common safety requirements of high-power and high-voltage devices. This effort focused on adapters provided by the driver, as these may present the highest safety and reliability risks. The recommendations made here apply to both retained and driver-provided adapters.
25 ENERGY STORAGE↗
Evaluating How Climate Adaptation Measures Affect the Interconnected Water‐Energy Resource Systems of the Western United States
Abstract The Western US faces increasing water stress from the impacts of climate change, making it difficult to meet water demands for the region's cities, agriculture, and hydropower generators. Existing literature suggests that climate adaptation measures such as water conservation, cropland retirement, wastewater recycling, and managed aquifer recharge can alleviate some of these challenges. Few analyses, however, compare the relative efficacy and system‐wide effects of these adaptations under different climate projections across the entire Western United States. Here we use a Western US‐wide water systems model to evaluate, by sector and sub‐region, how the widespread implementation of these adaptive measures impacts water demands, water deliveries, and electricity use related to the water system for three different climate projections. We find that wastewater recycling has greater potential to lower unmet indoor water demands than urban indoor water conservation measures. However, when implemented at scale, indoor water conservation reduces electricity use by an average of 683 Terawatt hours while wastewater recycling increases energy use by an average of 721 Terawatt hours, cumulatively from 2020 to 2070. Cropland retirement and aquifer recharge adaptations increase the ability to meet agricultural water demand, increase groundwater storage, and reduce summertime electricity use. While most of these findings are consistent across different climate projections, the benefits of aquifer recharge are sensitive to spatial variation of precipitation. Given the limitations and tradeoffs of each individually, the results suggest that a portfolio of adaptation measures will be needed for a climate‐resilient water and energy future in the Western US. Plain Language Summary The Western US faces increased water stress from the impacts of climate change, making it difficult to meet demands for cities, agriculture, and hydropower facilities. Adaptation measures like water conservation, retiring agricultural lands, recycling wastewater, and storing water underground can address these challenges. However, there is little modeling to understand the impact of these adaptations if they were implemented across the entire Western US while also considering climate change. We use a Western US‐wide water systems model to evaluate how implementing adaptation measures impacts groundwater levels, the ability to meet water demands, and electricity use related to water in three different possible climate futures. We find that recycling wastewater to drinking water standards does a better job of meeting urban water demands than water conservation measures. However, indoor water conservation reduces energy use for water while recycling wastewater increases energy use for water. Retiring agricultural lands and storing water underground both increase the ability to meet agricultural water demands, increase underground water storage, and reduce summertime energy use. No adaptation measures provides benefits across every metric we track. Therefore, multiple adaptation measures will likely be needed to achieve a climate‐resilient future for energy and water in the Western US. Key Points Water‐related climate change adaptations have different benefits and tradeoffs for interconnected water‐energy systems in the Western U.S. Wastewater recycling most increases urban water coverage, but has a significant tradeoff in the form of greater electricity use Cropland retirement and aquifer recharge benefit water and electricity systems most in the summer when those systems are most stressed
Singhal, A↗
Accelerated basis adaptation in homogeneous chaos spaces
Polynomial chaos expansions (PCE) provide an efficient approach to uncertainty quantification (UQ) and have been adapted to diverse applications across the spectrum of science and engineering. For situations involving large stochastic parameterizations, the curse of dimensionality renders PCE-based methods computationally prohibitive. A basis adaptation approach for PCE was proposed by Tipireddy and Ghanem (2014) which transforms the input random variables through an isometry such that sufficient probabilistic characterization of specific quantities of interest (QoI) is concentrated in an algebraic manifold embedded in the linear span of the dominant transformed variables. While quite versatile, that original version of the PCE basis adaptation exhibited slow convergence for a number of problems of practical significance. In the present paper, we propose two novel methods to accelerate the convergence of the original basis adaptation approach, thus expanding its reach while also providing insight into its performance. In the first method, information gained from a pilot PCE representation is used to correct the mean and Gaussian coefficients in the adapted space. By taking advantages of probabilistic information in higher dimensional adaptation gleaned from an initial adaptation, the second method updates the rotation matrix used to identify the dominant transformed variables. In this manner, the new rotation matrix concentrates even more probabilistic information in its first few dimensions. These two method can be combined to achieve even better performance, the combined method is referred to as sequentially optimized adaptation method. Here, the methods are demonstrated on an analytical test function and a model of a space structure with several sub-components and a non-smooth quantity of interest representing the maximum acceleration over time. Both methods achieve accelerated convergence of the basis adaptation approach with negligible additional costs.
Accelerated convergence↗
hr-Adaptivity for nonconforming high-order meshes with the target matrix optimization paradigm
In this study, we present an \(hr\) -adaptivity framework for optimization of high-order meshes. This work extends the r -adaptivity method by Dobrev et al. (Comput Fluids, 2020), where we utilized the Target-Matrix Optimization Paradigm (TMOP) to minimize a functional that depends on each element’s current and target geometric parameters: element aspect-ratio , size , skew , and rotation . Since fixed mesh topology limits the ability to achieve the target size and aspect-ratio at each position, in this paper, we augment the r -adaptivity framework with nonconforming adaptive mesh refinement to further reduce the error with respect to the target geometric parameters. The proposed formulation, referred to as \(hr\) -adaptivity, introduces TMOP-based quality estimators to satisfy the aspect-ratio target via anisotropic refinements and size target via isotropic refinements in each element of the mesh. The methodology presented is purely algebraic, extends to both simplices and hexahedra/quadrilaterals of any order, and supports nonconforming isotropic and anisotropic refinements in 2D and 3D. Using a problem with a known exact solution, we demonstrate the effectiveness of \(hr\) -adaptivity over both r - and \(h\) -adaptivity in obtaining similar accuracy in the solution with significantly fewer mesh nodes. We also present several examples that show that \(hr\) -adaptivity can help satisfy geometric targets even when \(r\) -adaptivity fails to do so, due to the topology of the initial mesh.
42 ENGINEERING↗
Adaptive protection opportunities, gap assessments, and designs
This report provides a comprehensive overview of adaptive protection schemes in use by distribution systems for protection, switching and control on their systems. A significant focus is placed on how existing schemes can be impacted by increasing penetrations of DER as well as how these schemes can enable DER penetrations to increase. EPRI have conducted a survey of member utilities and performed a comprehensive literature review with the goal of baselining the research and identifying gaps with a focus on the issues that were encountered with adaptive protection on real systems. The five adaptive protection applications that are most prevalent on systems today are discussed in detail. These are weather-based fuse-saving, adaptive protection to reduce short-circuit current, adaptive protection for DER, adaptive protection for microgrids, and distribution automation. A broad overview of the technology is given for each scheme. Issues that have been encountered by utilities are highlighted and the safety and reliability impacts are also examined. As distribution systems, intelligent electronic devices, grid equipment and distribution management systems are rapidly evolving, adaptive protection techniques and technologies will become more widely adopted. This report proposes a framework for a conceptual automatic adaptive protection system. EPRI have ongoing research, development and demonstration projects in all of the constituent elements, however challenges remain to link the elements together in a secure and reliable way. EPRI will continue research into automated adaptive protection applications and challenges for the systems of today and future applications to assist system operators in managing the evolving system.
14 SOLAR ENERGY↗
Local adaptation of both plant and pathogen: an arms‐race compromise in switchgrass rust
In coevolving species, parasites locally adapt to host populations as hosts locally adapt to resist parasites. Parasites often outpace host local adaptation since they have rapid life cycles, but host diversity, the strength of selection, and external environmental influence can result in complex outcomes. To better understand local adaptation in host–parasite systems, we examined locally adapted switchgrass (Panicum virgatum), and its leaf rust pathogen (Puccinia novopanici) across a latitudinal range in North America. We grew switchgrass genotypes in 10 replicated multiyear common gardens, measuring rust severity from natural infection in a ‘host reciprocal transplant’ framework for testing local adaptation. We conducted genome-wide association mapping to identify genetic loci associated with rust severity. Genetically differentiated rust populations were locally adapted to northern and southern switchgrass, despite host local adaptation to environmental conditions in the same regions. Rust resistance was polygenic, and distinct loci were associated with rust severity in the north and south. We narrowed a previously identified large-effect quantitative trait locus for rust severity to a candidate YELLOW STRIPE-LIKE gene and linked numerous other loci to defense-related genes. Overall, our results suggest that both hosts and parasites can be simultaneously locally adapted, especially when parasites impose less selection than other environmental factors.
59 BASIC BIOLOGICAL SCIENCES↗
Expectations of Future Natural Hazards in Human Adaptation to Concurrent Extreme Events in the Colorado River Basin
Human adaptation to climate change is the outcome of long-term decisions continuously made and revised by local communities. Adaptation choices can be represented by economic investment models in which the often large upfront cost of adaptation is offset by the future benefits of avoiding losses due to future natural hazards. In this context, we investigate the role that expectations of future natural hazards have on adaptation in the Colorado River basin of the USA. We apply an innovative approach that quantifies the impacts of changes in concurrent climate extremes, with a focus on flooding events. By including the expectation of future natural hazards in adaptation models, we examine how public policies can focus on this component to support local community adaptation efforts. Findings indicate that considering the concurrent distribution of several variables makes quantification and prediction of extremes easier, more realistic, and consequently improves our capability to model human systems adaptation. Hazard expectation is a leading force in adaptation. Even without assuming increases in exposure, the Colorado River basin is expected to face harsh increases in damage from flooding events unless local communities are able to incorporate climate change and expected increases in extremes in their adaptation planning and decision making.
54 ENVIRONMENTAL SCIENCES↗
Angular-spatial hp -adaptivity for radiative transfer with discontinuous Galerkin spectral element methods
Radiative transfer is important for many science and engineering applications, and numerical simulations of radiative transfer can be challenging. For instance, the radiation field is seven-dimensional – three spatial, two angular, one wavelength, and one temporal – and often features steep gradients. Therefore, memory usage is a key issue. To reduce memory, some past work has investigated the use of adaptive mesh refinement (AMR), typically for either the spatial or angular coordinate, and typically for only h -adaptivity. Here, we propose the use of AMR for the spatial and angular coordinates together, and the use of h - and p -adaptivity together as hp -AMR for the potential for further memory savings. We implemented the proposed method for several test cases in two spatial and one angular dimension, with the discontinuous Galerkin spectral element method. These test cases featured highly anisotropic angular radiation, with or without steep spatial gradients. Our primary findings from these test cases were: (1) Angular hp -adaptivity can deliver the radiation solution with the same accuracy as, and with much less computational memory than, uniform angular h - or p -refinements, or angular h -adaptivity alone. This is most obvious when the incoming radiation is highly anisotropic, in which case the savings can be orders of magnitude. (2) Full spatial-angular hp -adaptivity is more efficient in solution representation, compared to solely spatial or solely angular -adaptivity. This is most evident when steep gradients are present in both the spatial and angular distribution. These results suggest that adaptive spatial- hp angular-refinement may perform well in large-scale seven-dimensional applications.
Adaptive refinement↗
Reducing measurement costs by recycling the Hessian in adaptive variational quantum algorithms
Abstract Adaptive protocols enable the construction of more efficient state preparation circuits in variational quantum algorithms (VQAs) by utilizing data obtained from the quantum processor during the execution of the algorithm. This idea originated with Adaptive Derivative-Assembled Problem-Tailored variational quantum eigensolver (ADAPT-VQE), an algorithm that iteratively grows the state preparation circuit operator by operator, with each new operator accompanied by a new variational parameter, and where all parameters acquired thus far are optimized in each iteration. In ADAPT-VQE and other adaptive VQAs that followed it, it has been shown that initializing parameters to their optimal values from the previous iteration speeds up convergence and avoids shallow local traps in the parameter landscape. However, no other data from the optimization performed at one iteration is carried over to the next. In this work, we propose an improved quasi-Newton optimization protocol specifically tailored to adaptive VQAs. The distinctive feature in our proposal is that approximate second derivatives of the cost function are recycled across iterations in addition to optimal parameter values. We implement a quasi-Newton optimizer where an approximation to the inverse Hessian matrix is continuously built and grown across the iterations of an adaptive VQA. The resulting algorithm has the flavor of a continuous optimization where the dimension of the search space is augmented when the gradient norm falls below a given threshold. We show that this inter-optimization exchange of second-order information leads the approximate Hessian in the state of the optimizer to be consistently closer to the exact Hessian. As a result, our method achieves a superlinear convergence rate even in situations where the typical implementation of a quasi-Newton optimizer converges only linearly. Our protocol decreases the measurement costs in implementing adaptive VQAs on quantum hardware as well as the runtime of their classical simulation.
Ramôa, Mafalda (ORCID:0000000302187801)↗
Volumetric Rendering on Wavelet-Based Adaptive Grid
Numerical modeling of physical phenomena frequently involves processes across a wide range of spatial and temporal scales. In the last two decades, the advancements in wavelet-based numerical methodologies to solve partial differential equations, combined with the unique properties of wavelet analysis to resolve localized structures of the solution on dynamically adaptive computational meshes, make it feasible to perform large-scale numerical simulations of a variety of physical systems on a dynamically adaptive computational mesh that changes both in space and time. Volumetric visualization of the solution is an essential part of scientific computing, yet the existing volumetric visualization techniques do not take full advantage of multi-resolution wavelet analysis and are not fully tailored for visualization of a compressed solution on the wavelet-based adaptive computational mesh. Our objective is to explore the alternatives for the visualization of time-dependent data on space-time varying adaptive mesh using volume rendering while capitalizing on the available sparse data representation. Two alternative formulations are explored. The first one is based on volumetric ray casting of multi-scale datasets in wavelet space. Rather than working with the wavelets at the finest possible resolution, a partial inverse wavelet transform is performed as a preprocessing step to obtain scaling functions on a uniform grid at a user-prescribed resolution. As a result, a solution in physical space is represented by a superposition of scaling functions on a coarse regular grid and wavelets on an adaptive mesh. An efficient and accurate ray casting algorithm is based just on these coarse scaling functions. Additional details are added during the ray tracing by taking an appropriate number of wavelets into account based on support overlap with the interpolation point, wavelet coefficient magnitude, and other characteristics, such as opacity accumulation (front to back ordering) and deviation from frontal viewing direction. The second approach is based on complementing of wavelet-based adaptive mesh to the traditional Adaptive Mesh Refinement (AMR) mesh. Both algorithms are illustrated and compared to the existing volume visualization software for Rayleigh-Benard thermal convection and electron density data sets in terms of rendering time and visual quality for different data compression of both wavelet-based and AMR adaptive meshes.
Vezolainen, Alexei V.↗
A parallel p ‐adaptive discontinuous Galerkin method for the Euler equations with dynamic load‐balancing on tetrahedral grids
Abstract A novel p ‐adaptive discontinuous Galerkin (DG) method has been developed to solve the Euler equations on three‐dimensional tetrahedral grids. Hierarchical orthogonal basis functions are adopted for the DG spatial discretization while a third order TVD Runge‐Kutta method is used for the time integration. A vertex‐based limiter is applied to the numerical solution in order to eliminate oscillations in the high order method. An error indicator constructed from the solution of order and is used to adapt degrees of freedom in each computational element, which remarkably reduces the computational cost while still maintaining an accurate solution. The developed method is implemented with under the Charm++ parallel computing framework. Charm++ is a parallel computing framework that includes various load‐balancing strategies. Implementing the numerical solver under Charm++ system provides us with access to a suite of dynamic load balancing strategies. This can be efficiently used to alleviate the load imbalances created by p ‐adaptation. A number of numerical experiments are performed to demonstrate both the numerical accuracy and parallel performance of the developed p ‐adaptive DG method. It is observed that the unbalanced load distribution caused by the parallel p ‐adaptive DG method can be alleviated by the dynamic load balancing from Charm++ system. Due to this, high performance gain can be achieved. For the testcases studied in the current work, the parallel performance gain ranged from 1.5× to 3.7×. Therefore, the developed p ‐adaptive DG method can significantly reduce the total simulation time in comparison to the standard DG method without p ‐adaptation.
97 MATHEMATICS AND COMPUTING↗