A new global search method for general contact problems is developed and implemented in a Lagrangian program. The proposed algorithm improves the grid (bucket) method by utilizing both multiple grids and an overflow linked list. Without these improvements the search efficiency of the original method deteriorates under such configulations that contacting nodes are distributed sparsely or packed closely in the computational domain. A numerical simulation of a debris impacting double shields is conducted to verify the utility and the efficiency of the present method. We also discuss antitangle forces which is required to continue the computation long enough to form a debris cloud after the first shield is perforated.