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The purpose of this study is to develop a new numerical algorithm to simulate the phase-field model.

First, the derivative of the temporal direction is discretized by a second-order linearized finite difference scheme where it conserves the energy stability of the mathematical model. Then, the isogeometric collocation (IGC) method is used to approximate the derivative of spacial direction. The IGC procedure can be applied on irregular physical domains. The IGC method is constructed based upon the nonuniform rational B-splines (NURBS). Each curve and surface can be approximated by the NURBS. Also, a map will be defined to project the physical domain to a simple computational domain. In this procedure, the partial derivatives will be transformed to the new domain by the Jacobian and Hessian matrices. According to the mentioned procedure, the first- and second-order differential matrices are built. Furthermore, the pseudo-spectral algorithm is used to derive the first- and second-order nodal differential matrices. In the end, the Greville Abscissae points are used to the collocation method.

In the numerical experiments, the efficiency and accuracy of the proposed method are assessed through two examples, demonstrating its performance on both rectangular and nonrectangular domains.

This research work introduces the IGC method as a simulation technique for the phase-field crystal model.

The aim of this paper is to classify suppliers into some clusters based on sustainability factors. However, there might be some unqualified suppliers and we should identify and remove those suppliers before clustering.

First, using fuzzy screening system, the authors identify and remove the unqualified suppliers. Then, the authors run their proposed clustering method. This paper proposes a data envelopment analysis (DEA) algorithm to cluster suppliers.

This paper presents a two-aspect DEA-based algorithm for clustering suppliers into clusters. The first aspect applied DEA to consider efficient frontiers and the second aspect applied DEA to consider inefficient frontiers. The authors examine their proposed clustering approach by a numerical example. The results confirmed that their method can cluster DMUs into clusters.

The main contributions of this paper are as follows: This paper develops a new clustering algorithm based on DEA models. This paper presents a new DEA model in inefficiency aspect. For the first time, the authors’ proposed algorithm uses fuzzy screening system and DEA to select suppliers. Our proposed method clusters suppliers of MPASR based on sustainability factors.