SUMMARYIt is observed that for the solution of thin beam and plate problems using the meshfree method of finite spheres, Gaussian and adaptive quadrature schemes are computationally inefficient. In this paper, we develop a novel technique in which the integration points and weights are generated using genetic algorithms and stored in a lookup table using normalized coordinates as part of an offline computational step. During online computations, this lookup table is used much like a table of Gaussian integration points and weights in the finite element computations. This technique offers significant reduction of computational time without sacrificing accuracy. Example problems are solved which demonstrate the effectiveness of the procedure.

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The dynamics of red blood cells (RBCs) is one of the major aspects of the cardiovascular system that has been studied intensively in the past few decades. The dynamics of biconcave RBCs are thought to have major influences in cardiovascular diseases, the problems associated with cardiovascular assistive devices, and the determination of blood rheology and properties. This article provides an overview of the works that have been accomplished in the past few decades and aim to study the dynamics of RBCs under different flow conditions. While significant progress has been made in both experimental and numerical studies, a detailed understanding of the behavior of RBCs is still faced with many challenges. Experimentally, the size of RBCs is considered to be a major limitation that allows measurements to be performed under conditions similar to physiological conditions. In numerical computations, researchers still are working to develop a model that can cover the details of the RBC mechanics as it deforms and moves in the bloodstream. Moreover, most of reported computational models have been confined to the behavior of a single RBC in 2-dimensional domains. Advanced models are yet to be developed for accurate description of RBC dynamics under physiological flow conditions in 3-dimensional regimes.

In this paper we discuss the application of the method of finite spheres (MFS) to the solution of shear deformable beam and plate problems. A computationally efficient technique is presented in which the integration points and weights are generated using a genetic algorithm and stored in a lookup table using normalized coordinates much like a table of Gauss integration points and weights. This technique offers a significant reduction of computational time while maintaining accuracy.

In this paper we develop the Point Collocation-based Method of Finite Spheres (PCMFS) to simulate the viscoelastic response of soft biological tissues and evaluate the effectiveness of model order reduction methods such as modal truncation, Hankel optimal model and truncated balanced realization techniques for PCMFS. The PCMFS was developed in [1] as a physics-based technique for real time simulation of surgical procedures. It is a meshfree numerical method in which discretization is performed using a set of nodal points with approximation functions compactly supported on spherical subdomains centered at the nodes. The point collocation method is used as the weighted residual technique where the governing differential equations are directly applied at the nodal points. Since computational speed has a significant role in simulation of surgical procedures, model order reduction methods have been compared for relative gains in efficiency and computational accuracy. Of these methods, truncated balanced realization results in the highest accuracy while modal truncation results in the highest efficiency.