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Structural topology optimization is computationally expensive due to the involvement of high-resolution mesh and repetitive use of finite element analysis (FEA) for computing the structural response. Since FEA consumes most of the computational time in each optimization iteration, a novel GPU-based parallel strategy for FEA is presented and applied to the large-scale structural topology optimization of 3D continuum structures.

A matrix-free solver based on preconditioned conjugate gradient (PCG) method is proposed to minimize the computational time associated with solution of linear system of equations in FEA. The proposed solver uses an innovative strategy to utilize only symmetric half of elemental stiffness matrices for implementation of the element-by-element matrix-free solver on GPU.

Using solid isotropic material with penalization (SIMP) method, the proposed matrix-free solver is tested over three 3D structural optimization problems that are discretized using all hexahedral structured and unstructured meshes. Results show that the proposed strategy demonstrates 3.1× –3.3× speedup for the FEA solver stage and overall speedup of 2.9× –3.3× over the standard element-by-element strategy on the GPU. Moreover, the proposed strategy requires almost 1.8× less GPU memory than the standard element-by-element strategy.

The proposed GPU-based matrix-free element-by-element solver takes a more general approach to the symmetry concept than previous works. It stores only symmetric half of the elemental matrices in memory and performs matrix-free sparse matrix-vector multiplication (SpMV) without any inter-thread communication. A customized data storage format is also proposed to store and access only symmetric half of elemental stiffness matrices for coalesced read and write operations on GPU over the unstructured mesh.

The case study is based on field research and also on secondary data. A primary survey is included in the case study. Simple frequency and factor analysis as statistical tools have been used.

Family businesses, like that of Kiran Rai’s, owning a local Mom and Pop store in an emerging city were faced with a serious problem of sustaining their businesses. These family businesses countered immense competition from: their own types, i.e. from other local Mom and Pop stores within the same cities; online stores; and the organised stores.The choice of the customers to buy goods from the neighbourhood shops has remained largely as an age-old tradition in the households. With the millennials and the Generation Z (Gen Z) exposed to an array of brands, can they become the first choice of young customers for shopping for all kinds of products and varieties? Can the local Mom and Pop stores spread their wings across the young generations, particularly the Millennials and Gen Z through inexpensive social media channels? What are their growth options? How can the social media serve this purpose? The case uses the social cognition theory and the use gratification theory to throw light on the new concept of Social Shopping.

The case is meant to be discussed in courses like Fundamentals of Marketing, Digital Marketing and Retail Marketing in a 90-min session in the Post Graduate as well as in the Working Executives’ Management programmes. The case analysis will expose the students to the use of social media and its benefits to the small businesses. The students will also be able to analyse and understand the different types of Online Consumers’ Shopping Personalities. This would enable them to strategize for different stages in the decision-making processes.