The contact detection between non-spherical particles is an important issue in the discrete element method (DEM). The non-spherical particles commonly used in DEM are ellipsoids or super-ellipsoids. Such particles possess convex shape functions. The determination of contact points can be reduced to a set of nonlinear partial differential equations by the Lagrange method. Then, the Newton-Raphson method is used to solve these equations. The Lagrange method's premise is that the shape function is convex. For heart-shaped particles with concave shape functions, Lagrange method is not applicable. In this study, the contact point between heart-shaped particles is determined by grid method. This method does not need to provide the initial guess point and does not need to solve the Jacobian inverse matrix. There is no divergence in the solution process, and no limit to the concavity or convexity of the shape function. The algorithm is stable and is a general method. In the MATLAB and C compiler environment, the contact points between super-ellipsoid particles are calculated by the grid method and Newton-Raphson method, respectively. The grid method takes 60 and 0.14 ms, respectively, and its computational efficiency is better than that of the Newton-Raphson method. The time consumption for contact point of heart-shaped particles is less than that of super-ellipsoid particles. The number of contact point between two concave particles may be bigger than one; for this case, accurate results can still be obtained via the grid method. The method given in this study is applicable to the simulation of soft or hard particle systems. In addition, the method is used to simulate the evolution of the super-ellipsoid system with boundary constraints under gravity, and the stability and applicability of grid method are verified. (C) 2019 Elsevier B.V. All rights reserved.