**Publications**

56. E. Gordeliy and A. P. Peirce, Enrichment strategies and convergence properties of the XFEM for hydraulic fracture problems, accepted Comp. Meth. in Appl. Mech. and Eng., 2014.

55. A Peirce, Modeling multi-scale processes in hydraulic fracture propagation using the implicit level set algorithm, accepted Comp. Meth. in Appl. Mech. and Eng., 2014.

54. E.V. Dontsov and A. P. Peirce, A New Technique for Proppant Schedule Design, Hydraulic Fracturing Journal, V 1, No. 3, 2014.

53. E. Detournay and A. Peirce, On
the moving boundary conditions for a Hydraulic Fracture*,
* International Journal of Engineering Science, 84, p 147–155,
2014.

52. A.P. Bunger and A.P. Peirce, Numerical Simulation of Simultaneous Growth of Multiple Interacting Hydraulic Fractures from Horizontal Wells, submitted to the ASCE Shale Energy Conference, Pittsburgh, 21-23 July, 2014.

51. A. P. Peirce and A.P. Bunger, Interference Fracturing: Non-Uniform Distributions of Perforation Clusters that Promote Simultaneous Growth of Multiple Hydraulic Fractures, accepted by the SPE Journal on 14 July 2014.

(link to Posting on UBC Circle Repository)

50. Lecampion B., Peirce A.P, Detournay E., Zhang X., Chen Z., Bunger A.P., Detournay C., Napier J., Abbas S., Garagash D., Cundall, P., 2013. The impact of the Near-Tip Logic on the Accuracy and Convergence Rate of Hydraulic Fracture Simulators Compared to Reference solutions. In: Effective and Sustainable Hydraulic Fracturing, AP Bunger, J McLennan and R Jeffrey (eds.), ISBN 978-953-51-1137-5, (Intech), Chapter 43, p855-873.

49.E. Gordeliy and A. P. Peirce, *Implicit
level set schemes for modeling hydraulic fractures using the XFEM*, Comp.
Meth. in Appl. Mech. and Eng., 266, p125-143, 2013.

48..E. Gordeliy and A. P. Peirce, *Coupling
schemes for modeling hydraulic fracture propagation using the XFEM*,
Comp. Meth. in Appl. Mech. and Eng., 253, p305-322, 2013.

47. A.P. Peirce and F. Rochinha,
*An
Integrated Extended Kalman Filter Implicit Level Set Algorithm for monitoring
Planar Hydraulic Fracture*, Inverse Problems, 28,(2012) 015009,
(22 pp).

46.A.P. Peirce, "A Hermite Cubic Collocation Scheme for Plane Strain Hydraulic Fracture Problems", Comp. Meth. in Appl. Mech. and Eng., 199, Issues 29-32, p1949-1962, 2010.

45. F. Rochinha and A. Peirce, "Monitoring Hydraulic Fractures: State Estimation using an Extended Kalman Filter", Inverse Problems, 26, 2, 025009, 17p, 2010.

44. J. I. Adachi, E. Detournay, and A. P. Peirce, "An
Analysis of Classical Pseudo-3D Model for Hydraulic Fracture with Equilibrium
Height Growth across Stress Barriers", Int. J. of Rock Mech. and Min.
Sci., 47, p 625-639, 2010. (MATLAB Code: ColP3D.m
and .pdf file from the Circle UBC
Digital Repository).

43. S. Pillay, M. Ward, A. Peirce, and T. Kolokolnikov "An Asymptotic Analysis of the Mean First Passage Time for Narrow Escape Problems: Part I: Two-Dimensional Domains, SIAM J. on Multiscale Modelling and Simulation, V8, No. 3, pp 803-835, 2010.

42. A.Peirce, H. Gu, and E. Siebrits, "Uniform asymptotic Green's functions for efficient modeling of cracks in elastic layers with relative shear deformation controlled by linear springs", Int. J. Num. and Anal. Meth. in Geomechanics, 33, 285-308, 2009.

41. A. Peirce and E. Detournay "An Eulerian Moving Front Algorithm with Weak-Form Tip Asymptotics for Modeling Hydraulically driven Fractures", Communications in Numerical Methods in Engineering, 25, 185-200, 2009.

40. A. Peirce and E. Detournay, "An Implicit Level Set Method for Modeling Hydraulically Driven Fractures", Computer Methods in Applied Mechanics and Engineering, 197, 2858-2885, 2008.

39. J. Adachi and A. P. Peirce, "Asymptotic Analysis of an Elasticity Equation for a Finger-Like Hydraulic Fracture", Journal of Elasticity, 90, 43-69, 2008.

38. B. Lecampion and A. Peirce, "Multipole Moment Decomposition for imaging hydraulic fractures from remote elastic data," Inverse Problems, 23, 1641-1658, 2007.

37. J. Adachi, E. Siebrits, A. Peirce, and J. Desroches, "Computer Simulation of Hydraulic Fractures", Int. J. of Rock Mech. and Min. Sci. & Geomech. Abstr., 44, 739-757, 2007.

36. S. L. Mitchell, R. Kuske, and A.P. Peirce, "An asymptotic framework for finite hydraulic fractures including leak-off", SIAM J. on Appl. Math., 67, Issue 2, 364-386, 2007.

35. S. L. Mitchell, R. Kuske, and A.P. Peirce, "An asymptotic framework for the analysis of hydraulic fractures: the impermeable case", ASME Journal of Applied Mechanics., 74, 365-372, 2007.

34. S. Salapaka and A. Peirce, "Analysis of a novel preconditioner for a class of p-dimensional lower rank extracted systems", Numerical Linear Algebra with Applications, 13, issue 6, 437-472, 2006.

33. A. Peirce, "Localized Jacobain ILU Preconditioners for Hydraulic Fractures", International Journal for Numerical Methods in Engineering", 65, 12, 1935-1946, 2006.

32. A. P. Peirce and E. Siebrits, "A dual mesh Multigrid preconditioner for the efficient solution of hydraulically driven fracture problems", International Journal for Numerical Methods in Engineering, 63, 13, 1797-1823, 2005.

31. S. Salapaka, A.Peirce and M.Dahleh., "Analysis of a circulant based preconditioner for a class of lower rank extracted systems", Numerical Linear Algebra with Applications, 12, 9-32, 2005.

30. E. Siebrits and A.P.Peirce, "An efficient multi-layer planar 3D fracture growth algorithm using a fixed mesh approach", International Journal for Numerical Methods in Engineering, 53, 691-717, 2002.

29. A. P. Peirce and E. Siebrits, "The scaled flexibility matrix method for the efficient solution of boundary value problems in 2D and 3D layered elastic media", Computer Methods in Applied Mechanics and Engineering, 190 (45), 5935-5956, 2001.

28. A. P. Peirce, and E. Siebrits, "Uniform asymptotic approximations for accurate modeling of cracks in layered elastic media", International Journal of Fracture", 110, 205-239, 2001.

27. B. Birgisson, E. Siebrits, and A. Peirce, "Elastodynamic Direct Boundary Element Methods with Enhanced Numerical Stability Properties", Int. J. Num. Meth. Eng., 46, 871-888, 1999.

26. E. Siebrits, B. Birgisson, A. Peirce and S.L. Crouch, "On the numerical stability of time domain boundary element methods", Int. J. for Blasting & Fragmentation, Vol. 14, No. 7, 1997.

25. E. Siebrits and A. Peirce, "Implementation and application of elastodynamic boundary element discretizations with improved stability properties", Engineering Computations: Int. J. for Computer-aided Eng.& Software, Volume 14, no 7, 1997.

24. A. Peirce and E. Siebrits, "Stability analysis and design of time stepping schemes for general elastodynamic boundary element models", Int. J. Num. Meth. Eng., Vol. 40, pp 319-342, 1997.

23. A. Peirce and E. Siebrits, "Stability analysis of model problems for elastodynamic boundary element discretizations", Numerical Methods for Partial Differential Equations, Vol. 12, pp 585-613, 1996.

22. M. Dahleh, A. Peirce, H. Rabitz, and V. Ramakrishna, "Control of Molecular Motion", Invited paper in Proceedings of the IEEE, Vol. 84, No. 1, pp. 7-15, 1996.

21. J. Xin, A. Peirce, P. Ortoleva, and J. Chadam, "Reactive flows in layered porous media, I. Homogenization of free boundary problems", Asymptotic Analysis Vol. 11, pp. 31-54, 1995.

20. A. Peirce and J.A.L. Napier, "A spectral multipole method for efficient solution of large-scale boundary element models in elastostatics", Int. J. Num. Meth. Eng., Vol. 38, pp. 4009-4034, 1995.

19. V. Ramakrishna, M. Salapaka, M. Dahleh, H. Rabitz, and A. Peirce, "Controllability of Molecular Systems," Physical Review A, Vol. 51, No. 2, pp. 960-966, 1995.

18. An L. and Peirce A., "A weakly nonlinear analysis of elasto-plastic-microstructure models", SIAM J. on Appl. Math., Vol. 55, No. 1, pp.136-155, 1995.

17. An, L. and Peirce, A., "The effect of microstructure on elastic-plastic models", SIAM J. on Appl. Mathematics, Vol. 54, No. 3, pp.708-730, 1994.

16. Q. Zhu, A. Peirce and J. Chadam, "Initiation of Shape instabilities of Free Boundaries in Planar Cauchy-Stephan Problems", The European Journal of Applied Mathematics, Vol. 4, 36-49, 1993.

15. J. Xin, A. Peirce, J. Chadam and P. Ortoleva , "Reactive flows in layered porous media II: stability of the reaction interface", SIAM Journal on Appl. Math., Vol. 53, No. 2., 1993.

14. A. Peirce, S. Spottiswoode, and J.A.L. Napier, "The spectral boundary element method: A new window on boundary elements in rock mechanics", Int. J. of Rock Mech. and Min. Sci.& Geomech. Abstr., Vol. 29, No. 4, pp. 379-400, 1992.

13. M.H.I. Baird, K. Aravamudan, N. V. Rama Rao, J. Chadam and A. P. Peirce, "Unsteady axial mixing by natural convection in a vertical column", AIChE J., Vol. 38, No. 11, pp. 1825-1834, 1992.

12. J. Chadam, A. Peirce, and H-M. Yin, "The blowup property of solutions to some Diffusion Equations with Localized Nonlinear Reactions", Journal of Mathematical Analysis and Applications, Vol. 169, No. 2, 313-328, 1992.

11. M. Dahleh, A. P. Peirce, and H. Rabitz, "Design Challenges for Control of Molecular Dynamics", IEEE Control Systems Magazine, Vol. 12, No. 2, pp. 93-94, April, 1992.

10. M. Dahleh and A. P. Peirce, "Numerical Solution of a Class of Parabolic Partial Differential Equations Arising in Optimal Control Problems with Uncertainty", Numerical Methods for Partial Differential Equations, Vol. 8, No. 1, pp. 77-95, Jan., 1992.

9. A.P. Peirce, "Efficient multigrid solution of boundary element models of cracks and faults", Int. J. Num. and Anal. Meth. in Geomechanics, Vol. 15, pp. 549-572, 1991.

8. J. Chadam, A. Peirce, and P. Ortoleva, "Stability of reactive flows in porous media: coupled porosity and viscosity changes", SIAM Journal on Applied Math., Vol. 51, No.3, pp. 684-692, 1991.

7. M. Dahleh, A. Peirce, and H. Rabitz, "Optimal Control of Uncertain Quantum Systems", Physical Review A, Vol. 42, No. 3, pp. 1065-1079, August, 1990.

6. A. Peirce, A. Askar and H. Rabitz, "Convergence properties of a class of boundary element approximations to linear diffusion problems with localized nonlinear reactions", Numerical Methods for Partial Differential Equations, Vol. 6, pp.75-108, 1990.

5. A. P. Peirce and H. Rabitz. "The effect of defect structures on chemically active surfaces: a continuum approach", Phys. Rev. B., Vol. 38, No. 3, pp. 1734-1753, 1988.

4. A. P. Peirce, M. Dahleh and H. Rabitz, "Optimal Control of Quantum Mechanical Systems: Existence, Numerical Approximations and Applications", Physical Review A, Vol. 37, No. 12, pp. 4950-4964, 15 June, 1988.

3. A. P. Peirce and H. Rabitz, "Modeling the effect of changes in defect geometry on chemically active surfaces by the boundary element technique", Surface Science, Vol. 202, pp. 32-57, 1988.

2. A. P. Peirce and H. Rabitz, "An analysis of the effect of defect structures on catalytic surfaces by the boundary element technique", Surface Science, Vol. 202, pp. 1-31, 1988.

1. A. Peirce and J.H. Prevost, "On the lack of convergence of unconditionally stable explicit rational Runge-Kutta Schemes", Computer Methods in Applied Mechanics and Engineering, 57, 171-180, 1986.