Computational Methods

Efficient and compatible computational methods are necessary for the computational models to work to their full capacity. The approach to address this issue is to develop flexible and efficient numerical methods for both atomistic and continuum level computational models and for systems containing multiple energy domains, multiple length scales, complex geometries, and moving boundaries. A focus of this research is developing meshless computational methods for solving partial differential equations. We have developed Finite Cloud and Boundary Cloud methods for solving both interior and exterior boundary value problems.




Related Publications:
  1. X. Jin, G. Li and N. R. Aluru, ``New Approximations and Collocation Schemes in the Finite Cloud Method'', Computers and Structures, vol. 83, no. 17-18, pp. 1366-1385, 2005. (full text)
  2. X. Jin, G. Li and N. R. Aluru,``Positivity Conditions in Meshless Collocation Methods'', Computer Methods in Applied Methods and Engineering, vol. 193, no. 12-14, pp. 1171-1202, 2004. (full text)
  3. G. Li, G. H. Paulino and N. R. Aluru, ``Coupling of the Meshfree Finite Cloud Method with the Boundary Element Method: A Collocation Approach'', Computer Methods in Applied Mechanics and Engineering, vol. 192, no. 20-21, pp. 2355-2375, 2003. (full text)
  4. G. Li and N. R. Aluru, ``A Boundary Cloud Method with a Cloud-by-cloud Polynomial Basis'', Engineering Analysis with Boundary Elements, vol. 27, no. 1, pp. 57-71, 2003. (full text)
  5. G. Li and N. R. Aluru,``Boundary Cloud Method: A Combined Scattered Point/Boundary Integral Approach for Boundary-Only Analysis'',Computer Methods in Applied Mechanics and Engineering, vol. 191, no. 21-22, pp. 2337-2370, 2002. (full text)
  6. X. Jin, G. Li and N. R. Aluru,``On the Equivalence Between Least-Squares and Kernel Approximation in Meshless Methods'', Computer Modeling in Engineering and Sciences, vol. 2, no. 4, pp. 447-462, 2001. (full text)
  7. N. Aluru and G. Li, ``Finite Cloud Method: A True Meshless Technique Based On A Fixed Reproducing Kernel Approximation'', International Journal of Numerical Methods in Engineering, vol. 50, no. 10, pp. 2373-2410, 2001. (full text)