@article{xie_li_qiao_2011, title={A finite element method for elasticity interface problems with locally modified triangulations}, volume={8}, number={2}, journal={International Journal of Numerical Analysis and Modeling}, author={Xie, H. and Li, Z. L. and Qiao, Z. H.}, year={2011}, pages={189–200} } @article{ito_qiao_toivanen_2008, title={A domain decomposition solver for acoustic scattering by elastic objects in layered media}, volume={227}, ISSN={["1090-2716"]}, DOI={10.1016/j.jcp.2008.06.015}, abstractNote={A finite element solution procedure is presented for accurately computing time-harmonic acoustic scattering by elastic targets buried in sediment. An improved finite element discretization based on trilinear basis functions leading to fourth-order phase accuracy is described. For sufficiently accurate discretizations 100 million to 1 billion unknowns are required. The resulting systems of linear equations are solved iteratively using the GMRES method with a domain decomposition preconditioner employing a fast direct solver. Due to the construction of the discretization and preconditioner, iterations can be reduced onto a sparse subspace associated with the interfaces. Numerical experiments demonstrate capability to evaluate the scattered field with hundreds of wavelengths.}, number={19}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Ito, Kazufumi and Qiao, Zhonghua and Toivanen, Jari}, year={2008}, month={Oct}, pages={8685–8698} } @article{ito_qiao_2008, title={A high order compact MAC finite difference scheme for the Stokes equations: Augmented variable approach}, volume={227}, ISSN={0021-9991}, url={http://dx.doi.org/10.1016/j.jcp.2008.05.021}, DOI={10.1016/j.jcp.2008.05.021}, abstractNote={This paper deals with the steady Stokes flow on a rectangular domain. A high order compact MAC finite difference scheme based on the staggered grid is developed for solving Stokes equations with a Dirichlet boundary condition on the velocity. A novel high order boundary treatment is developed via introducing a suitable augmented variable. The accuracy of the proposed method is demonstrated in test problems. Creeping flow solutions for driven cavity problem are obtained numerically and compared with published results.}, number={17}, journal={Journal of Computational Physics}, publisher={Elsevier BV}, author={Ito, Kazufumi and Qiao, Zhonghua}, year={2008}, month={Sep}, pages={8177–8190} } @inproceedings{ito_qiao_2008, title={A high order finite difference scheme for the Stokes equations}, volume={466}, DOI={10.1090/conm/466/09115}, booktitle={Moving interface problems and applications in fluid dynamics}, author={Ito, K. and Qiao, Z.}, year={2008}, pages={35–51} } @article{qiao_2008, title={Numerical investigations of the dynamical behaviors and instabilities for the Gierer-Meinhardt system}, volume={3}, number={2}, journal={Communications in Computational Physics}, author={Qiao, Z. H.}, year={2008}, pages={406–426} }