Engineering with Computers

This paper deals with developing a fast and robust numerical formulation to simulate a system of fractional PDEs. At the first stage, the time variable is approximated by a finite difference method with first-order accuracy. At the second stage, the spectral Galerkin method based upon the fractional Jacobi polynomials is employed to discretize the spatial variables. We apply a reduced-order method based upon the proper orthogonal decomposition technique to decrease the utilized computational time. The unconditional stability property and the order of convergence of the new technique are analyzed in detail. The proposed numerical technique is well known as the reduced-order spectral Galerkin scheme. Furthermore, by employing the Newton–Raphson method and semi-implicit schemes, the proposed method can be used for solving linear and nonlinear ODEs and PDEs. Finally, some examples are provided to confirm the theoretical results.

Here, we study the flow of energy between coupled simulators in a co-simulation environment using the concept of power bonds. We introduce energy residuals which are a direct expression of the coupling errors and, hence, the accuracy of co-simulation results. We propose a novel energy-conservation-based co-simulation method (ECCO) for adaptive macro step size control to improve accuracy and efficiency. In contrast to most other co-simulation algorithms, this method is non-iterative and only requires knowledge of the current coupling data. Consequently, it allows for significant speed-ups and the protection of sensitive information contained within simulator models. A quarter car model with linear and nonlinear damping serves as a co-simulation benchmark and verifies the capabilities of the energy residual concept: reductions in the errors of up to 93% are achieved at no additional computational cost.

In this study, we optimized artificial neural network (ANN) with imperialist competition algorithm (ICA) for the problem of slope stability design charts. To prepare training and testing datasets for the ANN and ICA–ANN predictive models, an extensive number of limit equilibrium analysis modelings (e.g., for the lower bound, LB, limit analysis and upper bound, UB, limit analysis) was conducted. The analyses were conducted using OptumG2 computer software and implemented on two-layered cohesive soil layer sets. For each of the LB and UB limit analysis, the database consisted of 320 training datasets and 80 testing datasets. Variables of the ICA algorithm such as the number of countries, the number of initial imperialists and the number of decades were optimized using a series of trial-and-error process. The input parameters that used thorough the OptumG2 finite element modeling (FEM) analysis include depth factor (i.e., the ratio of first soil layer thickness to the slope height), slope angle, undrained shear strength ratio where the output was taken dimensionless stability number. The estimated results for both of datasets (e.g., training and testing) from ANN and ICA–ANN models were assessed based on three known statistical indices namely value account for (VAF), root means squared error (RMSE), and coefficient of determination (R2). To evaluate the performance of proposed models, color intensity rating (CER) and total ranking method (TRM), i.e., based on the result of statistical indices, was used. After 72 trial-and-error processes (e.g., sensitivity analysis on some neurons) the optimal architecture of 3 × 6 × 1 were found for both of the ANN–UB and ANN–LB models. As a result, both models presented excellent performance, however according to the introduced ranking system the ICA–ANN model could slightly perform a better performance compared to ANN. Based on R2, RMSE and VAF values of (0.9999, 0.0107 and 99.9924) and (0.9991, 0.0102 and 99.9913), respectively, were found for training and testing of the optimized ICA–ANN–LB predictive model. Similarly, for the ICA–ANN–UB predictive model, values of (0.9984, 0.0129 and 99.9659) and (0.9984, 0.01047 and 99.9915) were obtained for the R2, RMSE and VAF of training and testing datasets, respectively. However, in the ANN model, the R2 and RMSE for both of the training and testing datasets were (0.9982 and 0.01815) and (0.9972 and 0.01748), respectively. This proves a better performance of the ICA–ANN model in predicting the behaviors of slope stability of cohesive soils and consequently more reliable design solution charts provided herein.

This paper presents a sketch-based volumetric decomposition framework using geometric reasoning to assist in hex meshing. The sketch-based user interface makes the framework user-friendly and intuitive, and the geometric reasoning engine makes the framework smarter and improves the usability. The system first generates a database that contains both the B-rep and 3D medial object to capture the exterior and interior of the input model, respectively. Next, the geometric reasoning process determines sweeping direction and two types of sweepable regions and provides visual aids to assist the user in developing decomposition solutions. The user conducts decomposition via the sketch-based user interface, which understands the user’s intent through freehand stroke inputs for smart decomposition. Imprint and merge operations are then performed on the decomposed model before passing it to the sweeping algorithm to create hex meshes. The proposed framework has been tested on industrial models.