International journal for numerical methods in. The proposed methodology naturally extends to immersed methods, such as the Material-Point Method (MPM), provided the background discretization is sufficiently smooth. Optimal transportation meshfree approximation schemes for fluid and plastic flows. Among the meshfree methods, the Optimal Transportation Meshfree (OTM) method proposed by Li and Ortiz in 38 provides a robust and efcient solution to predict the thermomechanical response of materials under extreme dynamic conditions, especially in adiabatic circumstances 3942. Explicit forms of the correction terms, which eliminate rank deficiency of the resulting stiffness matrices and ensure optimal convergence of the discrete formulation, are derived for C 0 -continuous linear and quadratic FEM, and C 1 -continuous quadratic Non-Uniform Rational B-Splines (NURBS). The framework makes use of first- and higher-order Taylor expansion of the integrands involved in the principle of virtual work, and the analytical integration of the resulting correction terms. Abstract We propose a framework to improve one-point quadrature and, more generally, reduced integration for finite element methods (FEM), Isogeometric Analysis (IGA), and immersed methods. Authors: Wang, Hao Liao, Huming Fan, Zongyue Fan, Jiang Stainier, Laurent Li, Xiaobai Li, Bo Award ID(s): 1652839 Publication Date: NSF-PAR ID.
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