In this paper, we design high-order Runge-Kutta discontinuous Galerkin (RKDG) methods with multi-resolution weighted essentially non-oscillatory (multi-resolution WENO) limiters to compute compressible steady-state pr...
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In this paper, we design high-order Runge-Kutta discontinuous Galerkin (RKDG) methods with multi-resolution weighted essentially non-oscillatory (multi-resolution WENO) limiters to compute compressible steady-state problems on triangular meshes. A troubled cell indicator extended from structured meshes to unstructured meshes is constructed to identify triangular cells in which the application of the limiting procedures is required. In such troubled cells, the multi-resolution WENO limiting methods are used to the hierarchical L^(2) projection polynomial sequence of the DG solution. Through using the RKDG methods with multi-resolution WENO limiters, the optimal high-order accuracy can be gradually reduced to first-order in the triangular troubled cells, so that the shock wave oscillations can be well suppressed. In steady-state simulations on triangular meshes, the numerical residual converges to near machine zero. The proposed spatial reconstruction methods enhance the robustness of classical DG methods on triangular meshes. The good results of these RKDG methods with multi-resolution WENO limiters are verified by a series of two-dimensional steady-state problems.
Net load forecasting is crucial for energy planning and facilitating informed decision-making regarding trade and load distributions. However, evaluating forecasting models' performance against benchmark models re...
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Accurate net load forecasting is vital for energy planning, aiding decisions on trade and load distribution. However, assessing the performance of forecasting models across diverse input variables, like temperature an...
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THE well-known ancient Chinese philosopher Lao Tzu(老子)or Laozi(6th~4th century BC during the Spring and Autumn period)started his classic Tao Teh Ching《道德经》or Dao De Jing(see Fig.1)with six Chinese characters:&...
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THE well-known ancient Chinese philosopher Lao Tzu(老子)or Laozi(6th~4th century BC during the Spring and Autumn period)started his classic Tao Teh Ching《道德经》or Dao De Jing(see Fig.1)with six Chinese characters:"道(Dao)可(Ke)道(Dao)非(Fei)常(Chang)道(Dao)",which has been traditionally interpreted as“道可道,非常道”or"The Dao that can be spoken is not the eternal Dao".
Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical methods to solve steady-state solutions of hyperbolic partial differential equations(PDEs).The Gauss-Seidel iterations and alternati...
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Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical methods to solve steady-state solutions of hyperbolic partial differential equations(PDEs).The Gauss-Seidel iterations and alternating sweeping strategy are used to cover characteristics of hyperbolic PDEs in each sweeping order to achieve fast convergence rate to steady-state solutions.A nice property of fixed-point fast sweeping WENO methods which distinguishes them from other fast sweeping methods is that they are explicit and do not require inverse operation of nonlinear local ***,they are easy to be applied to a general hyperbolic *** deal with the difficulties associated with numerical boundary treatment when high-order finite difference methods on a Cartesian mesh are used to solve hyperbolic PDEs on complex domains,inverse Lax-Wendroff(ILW)procedures were developed as a very effective approach in the *** this paper,we combine a fifthorder fixed-point fast sweeping WENO method with an ILW procedure to solve steadystate solution of hyperbolic conservation laws on complex computing *** experiments are performed to test the method in solving various problems including the cases with the physical boundary not aligned with the *** results show highorder accuracy and good performance of the ***,the method is compared with the popular third-order total variation diminishing Runge-Kutta(TVD-RK3)time-marching method for steady-state *** examples show that for most of examples,the fixed-point fast sweeping method saves more than half CPU time costs than TVD-RK3 to converge to steady-state solutions.
Attention is the brain's mechanism for selectively processing specific stimuli while filtering out irrelevant information. Characterizing changes in attention following long-term interventions (such as transcrania...
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The ability to manipulate light propagation sets the foundations for optical communication and information processing systems. With the ever-growing data capacity and data rate, photonic integrated circuits have attra...
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Multitasking requires rapid switching of attention and cognitive resources between different tasks in a dynamic environment, relying on cognitive processes, such as working memory, executive control, and selective att...
Net load forecasting is crucial for energy planning and facilitating informed decision-making regarding trade and load distributions. However, evaluating forecasting models' performance against benchmark models re...
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ISBN:
(数字)9798350352528
ISBN:
(纸本)9798350352535
Net load forecasting is crucial for energy planning and facilitating informed decision-making regarding trade and load distributions. However, evaluating forecasting models' performance against benchmark models remains challenging, thereby impeding experts' trust in the model's performance. In this context, there is a demand for technological interventions that allow scientists to compare models across various timeframes and solar penetration levels. This paper introduces a visual analytics-based application designed to compare the performance of deep-learning-based net load forecasting models with other models for probabilistic net load forecasting. This application employs carefully selected visual analytic interventions, enabling users to discern differences in model performance across different solar penetration levels, dataset resolutions, and hours of the day over multiple months. We also present observations made using our application through a case study, demonstrating the effectiveness of visualizations in aiding scientists in making informed decisions and enhancing trust in net load forecasting models.
Accurate net load forecasting is vital for energy planning, aiding decisions on trade and load distribution. However, assessing the performance of forecasting models across diverse input variables, like temperature an...
Accurate net load forecasting is vital for energy planning, aiding decisions on trade and load distribution. However, assessing the performance of forecasting models across diverse input variables, like temperature and humidity, remains challenging, particularly for eliciting a high degree of trust in the model outcomes. In this context, there is a growing need for data-driven technological interventions to aid scientists in comprehending how models react to both noisy and clean input variables, thus shedding light on complex behaviors and fostering confidence in the outcomes. In this paper, we present Forte, a visual analytics-based application to explore deep probabilistic net load forecasting models across various input variables and understand the error rates for different scenarios. With carefully designed visual interventions, this web-based interface empowers scientists to derive insights about model performance by simulating diverse scenarios, facilitating an informed decision-making process. We discuss observations made using Forte and demonstrate the effectiveness of visualization techniques to provide valuable insights into the correlation between weather inputs and net load forecasts, ultimately advancing grid capabilities by improving trust in forecasting models.
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