Computational Mechanics Lab

A new numerical approach to the solution of PDEs with optimal accuracy on irregular domains and Cartesian meshes. Part 1: the derivations for the wave, heat and Poisson equations in the 1-D and 2-D cases. Idesman, A. Archive of Applied Mechanics, 2020, 1-28, https://doi.org/10.1007/s00419-020-01744-w

 

A new numerical approach to the solution of PDEs with optimal accuracy on irregular domains and Cartesian meshes. Part 2: numerical simulation and comparison with FEM. Dey, B. and Idesman, A. Archive of Applied Mechanics, 2020, 1-26, https://doi.org/10.1007/s00419-020-01742-y

 

A high-order numerical approach with cartesian meshes for modeling of wave propagation and heat

transfer on irregular domains with inhomogeneous materials., Idesman A. and Dey B. Computer Methods in Applied Mechanics and Engineering, 2020, 370, 113249, pp. 1-22, https://doi.org/10.1016/j.cma.2020.113249

 

New 25-point stencils with optimal accuracy for 2-D heat transfer problems. Comparison with the quadratic isogeometric elements. Idesman, A. and Dey, B Computational Physics, 2020, 418, 113249, pp. 1-34, https://doi.org/10.1016/j.jcp.2020.109640

 

The treatment of the Neumann boundary conditions for a new numerical approach to the solution of PDEs with optimal accuracy on irregular domains and Cartesian meshes., Idesman A. and Dey B. Computer Methods in Applied Mechanics and Engineering, 2020, 365, 112985, pp. 1-25, https://doi.org/10.1016/j.cma.2020.112985

 

A new numerical approach to the solution of the 2-D Helmholtz equation with optimal accuracy on irregular domains and Cartesian meshes., Idesman A. and Dey B. Computational Mechanics, 2020, 65, pp.11891204, https://doi.org/10.1007/s00466-020-01814-4 

 

Compact high-order stencils with optimal accuracy for numerical solutions of 2-D time-independent elasticity equations., Idesman A. and Dey B. Computer Methods in Applied Mechanics and Engineering, 2020, 360, 112699, pp. 1-17, https://doi.org/10.1016/j.cma.2019.112699

 

Accurate numerical solutions of 2-D elastodynamics problems using compact high-order stencils., Idesman A. and Dey B. Computer and Structures, 229 (2020) 106160, https://doi.org/10.1016/j.compstruc.2019.106160

 

A new 3-D numerical approach to the solution of PDEs with optimal accuracy on irregular domains and Cartesian meshes., Idesman A. and Dey B. Computer Methods in Applied Mechanics and Engineering, 2019, 354, pp. 568-592, https://doi.org/10.1016/j.cma.2019.05.049

 

The use of the local truncation error to improve arbitrary-order finite elements for the linear wave and heat equations., Idesman A. Computer Methods in Applied Mechanics and Engineering, 2018, 334, pp. 268-312, https://doi.org/10.1016/j.cma.2018.02.001

 

The use of the local truncation error for the increase in accuracy of the linear finite elements for heat transfer problems. Idesman A.V. and Dey B. Computer Methods in Applied Mechanics and Engineering, 2017, 319, pp. 52 - 82, https://doi.org/10.1016/j.cma.2017.02.013

Optimal Reduction of Numerical Dispersion for Wave Propagation Problems. Part 2: Application to 2-D Isogeometric Elements. Idesman A.V. and Dey B.   Computer Methods in Applied Mechanics and Engineering, 2017, 321, pp. 235268, https://doi.org/10.1016/j.cma.2017.04.008

 

Optimal Reduction of Numerical Dispersion for Wave Propagation Problems. Part 1: Application to 1-D Isogeometric Elements. Idesman A.V. Computer Methods in Applied Mechanics and Engineering, 2017, 317, pp. 970 - 992, https://doi.org/10.1016/j.cma.2017.01.014

 

Accurate finite element simulation of stresses for stationary dynamic cracks under impact loading, Idesman A.V., Bhuiyan A., Foley J. Finite Elements in Analysis and Design, 2017, 126, pp. 26 - 38, https://doi.org/10.1016/j.finel.2016.12.004

 

Accurate finite element modeling of wave propagation in composite and functionally graded materials, Idesman A.V. Composite Structures, 2014, 117, pp. 298-308.

 

Finite element modeling of linear elastodynamics problems with explicit time-integration methods and linear elements with the reduced dispersion error. Idesman A.V. and Pham D. Computer Methods in Applied Mechanics and Engineering, 2014, 271, pp. 86 -108.

 

Accurate finite element modeling of acoustic waves, Idesman A.V. and Pham D.  Computer Physics Communications, 2014, 185, pp. 2034-2045.

 

Accurate finite element simulation and experimental study of elastic wave propagation in a long cylinder under impact loading. Idesman A. V. and Mates S. P.  International Journal of Impact Engineering, 2014, 71, pp. 1-16.

 

Accurate solutions of wave propagation problems under impact loading by the standard, spectral and isogeometric high-order finite elements. Comparative study of accuracy of different space-discretization techniques, Idesman A.V., Pham D., Foley J., Schmidt M.  Finite Elements in Analysis and Design, 2014, 88, pp. 67 - 89.

 

Use of post-processing to increase the order of accuracy of the trapezoidal rule at time integration of linear elastodynamics problems, Idesman A.V. Computational Physics, 2012, 231, pp. 3143-3165.

 

Finite element simulations of dynamics of multivariant martensitic phase transitions based on Ginzburg-Landau theory, Cho J.-Y., Idesman A.V., Levitas V.I., Park T. International Journal of Solids and Structures, 2012, 49, pp. 1973-1992.

 

A new exact, closed-form a-priori global error estimator for second- and higher-order time integration methods for linear elastodynamics, Idesman A.V. International Journal For Numerical Methods In Engineering, 2011, 88, pp. 1066-1084.

 

Accurate 3-D finite element simulation of elastic wave propagation with the combination of explicit and implicit time-integration methods, Idesman A.V., Schmidt M., and Foley J. R. Wave motion, 2011, 48, pp. 625-633.

 

Accurate time integration of linear elastodynamics problems, Idesman A.V. Computer Modeling in Engineering and Sciences, 2011, 71 (2), pp. 111-148.

 

Accurate finite element modeling of linear elastodynamics problems with the reduced dispersion error, Idesman A.V., Schmidt M., and Foley J. R. Computational Mechanics, 2011, 47, pp.555-572.

 

Phase field modeling of fracture in liquid, Levitas V.I., Idesman A.V. and Palakala A. K. Journal of Applied Physics, 2011, 110, pp. 033531 (1-9).

 

Finite element simulation of wave propagation in an axisymmetric bar, Idesman A.V., Subramanian

K., Schmidt M., Foley J. R., Tu Y., Sierakowski R. L. Journal of Sound and Vibration, 2010, 329, pp.2851-2872

 

Modeling of the effects different substrate materials on the residual thermal stresses for aluminum nitride crystal growth by sublimation, Lee R. G., Idesman A.V., Nyakiti L., Chaudhuri J. Journal of Applied Physics, 2009, 105, pp. 033521-6.

 

Benchmark problems for wave propagation in elastic materials, Idesman A.V., Samajder H., Aulisa E., Seshaiyer P. Computational Mechanics, 2009, 43 (6) pp. 797 - 814.

 

Finite element modeling of dynamics of martensitic phase transitions, Idesman A.V., Cho J.-Y., Levitas V.I. Applied Physics Letters, 2008, 93, pp. 043102.

 

A new explicit predictor-multicorrector high-order accurate method for linear elastodynamics, Idesman A.V., Schmidt M., Sierakowski R. L. Journal of Sound and Vibration, 2008, 310, pp. 217-229.

 

 Distributed computational methods for coupled fluid-structure-thermal interaction applications, Aulisa E., Manservisi S., Seshaiyer P. and Idesman A.V. Journal of Algorithms & Computational Technology, 2008, pp. 8-15.

 

Modeling of residual stresses for aluminum nitride crystal growth by sublimation, Lee R. G., Idesman A.V., Nyakiti L., Chaudhuri J. Journal of Applied Physics, 2007, v 102, n 6, pp. 063525.

 

A new high-order accurate continuous Galerkin method for linear elastodynamics problems, Idesman A.V. Computational Mechanics, 2007, 40, pp. 261-279.

 

Solution of linear elastodynamics problems with space-time finite elements on structured and unstructured meshes, Idesman A.V. Computer Methods in Applied Mechanics and Engineering, 2007, 196, pp. 1787-1815.

 

Finite element simulations of martensitic phase transitions and microstructures based on a strain-softening model, Idesman A.V., Levitas V.I., Preston D.L., Cho J.-Y. Journal of the Mechanics and Physics of Solids, 2005, 53, pp. 495-523.

 

Microscale phase-field simulation of martensitic microstructure evolution, Levitas V.I., Idesman A.V., Preston D.L. Physical Review Letters, 2004, 93 (10), 105701(4).

 

Comparison of different isotropic elastoplastic models at finite strains used in numerical analysis, Idesman A.V. Computer Methods in Applied Mechanics and Engineering, 2003, 192(41-42), pp. 4659-4674.

Selected Publications