In this paper, we present a new splitting nearly-analytic symplectic partitioned Runge–Kutta (SNSPRK) method for the two-dimensional (2D) elastic wave equations. It is an extension to elastic wave equation of our recent work on the locally one-dimensional nearly-analytic symplectic partitioned Runge–Kutta (LOD-NSPRK) method for the 2D acoustic wave equations. The method is based on the spatial differential operator-split technique, in which the resulting spatial discrete matrices are symmetric unlike the conventional nearly-analytic symplectic partitioned Runge–Kutta (NSPRK) method. The stability condition is given, which has more relax restriction for the time step than the NSPRK schemes. To show the performance of the new method, numerical experiments are given. Numerical results illustrate that the SNSPRK method has better long-term calculation capability as time proceeds than the NSPRK method.

The segmentation and classification of brain tumor are a attractive regions, which distinguish tumor as well as nontumor cells for identifying a level of tumor. Segmentation and classification from MRI images is a great challenge due to their altering image sizes and vast databases. Various schemes are designed for the segmentation and classification of the brain tumor, but these methods failed to offer better classification accuracy and decision-making. Here, Circle-inspired sine cosine Optimization_conditional random field-recurrent neural network (CISCO-CRF-RNN) and CISCO-Zeiler and Fergus network (CISCO-ZFNet) are introduced for brain tumor segmentation and classification. A pre-processing phase in this research is executed by the median filter to eliminate noises from an image. The segmentation is done by CRF-RNN, which is trained by CISCO. Furthermore, CISCO is newly introduced by incorporation of Circle-Inspired Optimization Algorithm (CIOA) and Sine Cosine Algorithm (SCA). Thereafter, image augmentation is performed utilizing some image augmentation techniques, and thereafter, features namely statistical features, Convolutional Neural Network (CNN) features, haralick features, pyramid histogram of orientation gradients (PHoG), and Local Vector Pattern (LVP) are extracted. Finally, the classification of brain tumor is accomplished utilizing ZFNet, which is tuned using CISCO. In addition, CISCO-CRF-RNN obtained maximal segmentation accuracy of 90.6% whereas CISCO-ZFNet achieved maximum pixel accuracy, negative predictive value (NPV), positive predictive value (PPV), and True positive rate TPR of 92.5%, 89.2%, 90.1% and 93% as well as minimum FNR of 15%.

In this paper, by applying the accelerated technique and relaxation two-sweep strategy to the modulus-based matrix splitting iteration method, we establish the accelerated relaxation two-sweep modulus-based matrix splitting method. The proposed method contains the accelerated modulus-based matrix splitting and the generalized accelerated modulus-based matrix splitting methods presented recently as special cases. Compared with some existing methods, the proposed method can use more information during each iteration, which may lead to higher computational efficiency. We investigate the convergence properties of the new method, and prove that it is convergent under certain assumptions. Also, for the accelerated relaxation two-sweep modulus-based accelerated overrelaxation method, we analyze the convergence regions of the parameters in detail. Numerical examples are offered to show that the proposed method is efficient and performs better than the generalized accelerated modulus-based matrix splitting one in actual implementation.

Scattering problems have wide applications in the medical and military fields. In this paper, the weighted least-squares (WLS) collocation method based on radial basis functions (RBFs) is developed to solve elastic wave scattering problems, which are governed by the Navier equation and the Helmholtz equations with coupled boundary conditions. The perfectly matched layer (PML) technique is used to truncate the unbounded domain into a bounded domain. The WLS method is constructed by setting the collocation points denser than the trial centers and imposing different weights on different types of boundary conditions. The WLS method can overcome the matrix singularity problem encountered in the Kansa method, and the convergence rate of WLS is [Formula: see text] for Sobolev kernel with kernel smoothness [Formula: see text]. Furthermore, compared with the finite element method (FEM) and the Kansa method, WLS can provide higher accuracy and more stable solutions for relatively large angular frequencies. The numerical example with a circular obstacle is used to verify the effectiveness and convergence behavior of the WLS. Besides, the proposed scheme can easily handle irregular obstacles and obtain stable results with high accuracy, which is validated through experiments with ellipse and kite-shaped obstacles.

In this paper, a new boundary-conforming adaptive method for the numerical integration of trimmed elements is presented. The locations and weights of new integration points are determined based on special mapping formulations. The prerequisite of this technique is to describe the trimming curves/surfaces by parametric Bezier curves/surfaces within the parent element domain. The fitting error is under control, therefore the number of quadrature points for exact integration can be adjusted automatically based on the complexity of trimming curve and the corresponding integrand. The proposed method can be easily implemented into fictitious domain approaches. Different integration tasks as well as structural examples reveal that the proposed method delivers accurate and robust solutions for a wide variety of 2D/3D geometries with a rather low number of integration points.

In this paper, we address the identification of an unknown inclusion in an elliptic equation, which arises in the context of electrical impedance tomography and multiphase problems. We present a novel approach by formulating the overdetermined system as an optimal design problem based on the unknown inclusion and two state solutions, which is derived from by introducing a least square functional. We establish the existence results and first optimality conditions, and employ the finite element method to discretize the involved variational equations. Furthermore, we update the unknown inclusion using the level-set method. To demonstrate the effectiveness and validity of our proposed algorithm, we investigate simple and complex geometries numerically. Our results showcase the efficiency and accuracy of the method, making it a promising tool for solving similar inverse problems in various engineering applications.