Publications:

Journal papers:

• X. Li and W. Wang, A high order discontinuous Galerkin method for the recovery of the conductivity in Electrical Impedance Tomography, Journal of Computational and Applied Mathematics, v434(2023), 115344.

• B. Dong and W. Wang, Numerical investigations on the resonance errors of multiscale discontinuous Galerkin methods for one-dimensional stationary Schrödinger equation, Communications on Applied Mathematics and Computation, 2023.

• B. Dong and W. Wang, A high-order multiscale discontinuous Galerkin method for two-dimensional Schrödinger equation in quantum transport, Journal of Computational and Applied Mathematics, v418(2023), pp. 1-14.

• B. Dong and W. Wang, High-order multiscale discontinuous Galerkin methods for the one-dimensional stationary Schrodinger equation, Journal of Computational and Applied Mathematics, v380(2020), pp. 1-11.

• W. Wang and D. Kelly, A high-order PIC method for advection-dominated flow with application to shallow water waves, International Journal for Numerical Methods in Fluids, v87(2018), pp. 583-600.

• B. Dong, C.-W. Shu and W. Wang, A new multiscale discontinuous Galerkin method for the one-dimensional stationary Schrodinger equation, Journal of Scientific Computing, v66(2016), pp. 321-345.

• W. Wang, C.-W. Shu, H. C. Yee, D. V. Kotov and B. Sjögreen, High order finite difference methods with subcell resolution for stiff multispecies detonation capturing, Communications in Computational Physics, v17(2015), pp. 317-336.

• Y. Zhang, W. Wang, J. Guzmán and C.-W. Shu, Multi-scale discontinuous Galerkin method for solving elliptic problems with curvilinear unidirectional rough coefficients, Journal of Scientific Computing, v61(2014), pp. 42-60.

• H. C. Yee, D. V. Kotov, W. Wang and C.-W. Shu, Spurious behavior of shock-capturing methods: problems containing stiff source terms and discontinuities, Journal of Computational Physics, v241(2013), pp. 266-291.

• W. Wang, C.-W. Shu, H. C. Yee and B. Sjögreen, High order finite difference methods with subcell resolution for advection equations with stiff source terms, Journal of Computational Physics, v231(2012), pp. 190-214.

• W. Wang, H. C. Yee, B. Sjögreen, T. E. Magin and C.-W. Shu, Construction of low dissipative high order well-balanced filter schemes for non-equilibrium flow, Journal of Computational Physics, v230(2011), pp. 4316-4335.

• W. Wang, J. Guzmán and C.-W. Shu, The multiscale discontinuous Galerkin method for solving a class of second order elliptic problems with rough coefficients, International Journal of Numerical Analysis and Modeling, v8(2011), pp. 28-47.

• W. Wang, C.-W. Shu, H.C. Yee and B. Sjögreen, High order well-balanced schemes and applications to non-equilibrium flow, Journal of Computational Physics, v228(2009), pp. 6682--6702.

• W. Wang and C.-W. Shu, The WKB local discontinuous Galerkin method for the simulation of Schrodinger equation in a resonant tunneling diode, Journal of Scientific Computing, v40(2009), pp. 360-374.

• W. Wang, X. Li and C.-W. Shu, The discontinuous Galerkin method for the multiscale modeling of dynamics of crystalline solids, Multiscale Modeling and Simulation, v7(2008), pp. 294-320.

Conference papers:

• B. Dong and W. Wang, A new multiscale discontinuous Galerkin method for a class of second-order equations with oscillatory solutions in two-dimensional space, ICOSAHOM 2020+1, Vienna, Austria, July 12-16, 2021.

• H. C. Yee, D. V. Kotov, W. Wang and C.-W. Shu, Spurious behavior of shock-capturing methods: problems containing stiff source terms and discontinuities, 7th International Conferences on Computational Fluid Dynamics (ICCFD7), Big Island, Hawaii, July 9-13, 2012.

• H. C. Yee, B. Sjögreen, C.-W. Shu, W. Wang, T. E. Magin and A. Hadjadj, On numerical methods for hypersonic turbulent flows, Proceedings of the 7th European Symposium on Aerothermodynamics, Brugge, Belgium, May 9-12, 2011.

Technical Reports:

• W. Wang, C.-W. Shu, H. C. Yee and B. Sjögreen, On well-balanced schemes for non-equilibrium flow with stiff source terms, Annual Research Briefs, Center for Turbulence Research, Stanford University (2008), pp. 391-402.

• W. Wang, H. C. Yee, B. Sjögreen, T. E. Magin and C.-W. Shu, Construction of low dissipative high order well-balanced filter schemes for non-equilibrium flow, Annual Research Briefs, Center for Turbulence Research, Stanford University (2009), pp. 409-421.

• W. Wang, C.-W. Shu, H. C. Yee and B. Sjögreen, High-order finite difference methods with subcell resolution for hyperbolic conservation laws with stiff reaction terms: preliminary results, Annual Research Briefs, Center for Turbulence Research, Stanford University (2010), pp. 149-160.

• W. Wang, C.-W. Shu, H. C. Yee and B. Sjögreen, High-order finite difference methods with subcell resolution for 2D detonation waves, Annual Research Briefs, Center for Turbulence Research, Stanford University (2011), pp. 371-380.

• D. V. Kotov, H. C. Yee, B. Sjögreen, W. Wang and C.-W. Shu, Performance of four high-order shock-capturing schemes for stiff source terms with discontinuities: preliminary results, Annual Research Briefs, Center for Turbulence Research, Stanford University (2011), pp. 393-403.

• D. V. Kotov, H. C. Yee, W. Wang and C.-W. Shu, On spurious numerics in solving reactive equations, Annual Research Briefs, Center for Turbulence Research, Stanford University (2012).

Thesis:

• W. Wang, Multiscale discontinuous Galerkin methods and applications, Ph.D. Thesis, Brown University, 2008.

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