专著教材：
[1]. 任政勇, 汤井田, 潘克家, 邱乐稳, 王飞燕. 直流电阻率有限单元法及进展[M]. 北京：科学出版社, 2017.
[2]. 潘克家, 凌巍炜, 任政勇, 郑洲顺. 数据建模方法与案例[M]. 北京：科学出版社, 2022.
学术论文：
2023年
[1]. Li Z, Pan K*. High order compact schemes for flux type BCs. SIAM Journal on Scientific Computing, 2023, 45(2): A646-A674.
[2]. Hu S, Pan K*, Ren Z, et al. Fast large-scale gravity modeling using a high-order compact cascadic multigrid strategy. Geophysics, 2023, 86: G125–G140.
[3]. Ling W, Pan K*, Ren Z, et al. One-dimensional magnetotelluric parallel inversion using a ResNet1D-8 residual neural network. Computers & Geosciences, 2023: 105454.
[4]. Li J, Li Z, Pan K*. Accurate derivatives approximations and applications to some elliptic PDEs using HOC methods. Applied Mathematics and Computation, 2023, 459: 128265.
[5]. Fu K, Hu H, Pan K*. A sixth order quasi-compact finite difference method for Helmholtz equations with variable wave numbers. Applied Mathematics Letters, 2023, 146: 108805.
[6]. 潘克家, 韩旭, 王鹏德, 等. 基于非结构外推多重网格法的带地形二维大地电磁各向异性有限元正演. 石油地球物理勘探, 2023, 58: 454-468.
[7]. 王晋轩, 潘克家*, 王鹏德, 任政勇, 等. 大规模三维大地电磁各向异性正演的非均匀网格外推多重网格法. 地球物理学报, 2023, 66(10): 4301-4316.
[8]. Ali R, Pan K. New generalized Gauss-Seidel iteration methods for solving absolute value equations. Mathematical Methods in the Applied Sciences, 2023, DOI:10.1002/mma.9062.
[9]. Pan K, Fu K, Li J, Hu H. New Sixth-Order Compact Schemes for Poisson/Helmholtz Equations. Numerical Mathematics:Theory, Methods and Applications, 2023, 16(2): 393-409.
[10]. Yao H, Ren Z, Pan K, et al. A global mantle conductivity model derived from 8 years of Swarm satellite magnetic data. Earth and Planetary Physics, 2023, 7(1): 49-56.
[11]. Ali R, Pan K. The new iteration methods for solving absolute value equations. Applications of Mathematics, 2023, 68: 109–122.
[12]. Hu S, Pan K*, Wu X, et al. An efficient extrapolation multigrid method based on a HOC scheme on nonuniform rectilinear grids for solving 3D anisotropic convection-diffusion problems. Computer Methods in Applied Mechanics and Engineering, 2023, 403: 115724.
[13]. Wu P, Pan K*, Ling W, et al. An Efficient EXCMG-Newton Method Combined with Fourth-Order Compact Schemes for Semilinear Poisson Equations. East Asian Journal on Applied Mathematics, 2023, 13: 119-139.
2022年
[14]. Pan K, Wang J, Hu S, et al. An efficient cascadic multigrid solver for 3-D magnetotelluric forward modelling problems using potentials. Geophysical Journal International, 2022, 230(3): 1834-1851.
[15]. Pan K, Wu X, Hu H, et al. A new FV scheme and fast cell-centered multigrid solver for 3D anisotropic diffusion equations with discontinuous coefficients. Journal of Computational Physics, 2022, 449: 110794.
[16]. Pan K, Wu X, Xu Y, et al. An exact-interface-fitted mesh generator and linearity-preserving finite volume scheme for anisotropic elliptic interface problems. Journal of Computational Physics, 2022, 463: 111293.
[17]. Pan K, Li J, Wu X, et al. A new finite volume scheme with gradient transfer method for solving diffusion problems on the distorted hexahedral meshes. Computational Geosciences, 2022, 26(2): 279-294.
[18]. Ren Z, Zhang Y, Zhong Y, Pan K, Wu Q, Tang J. Magnetic anomalies caused by 3D polyhedral structures with arbitrary polynomial magnetization. Geophysical Research Letters, 2022, 49(18): e2022GL099209.
[19]. Pan K, Wu X, Yu Y, Sheng Z, Yuan G. Extrapolation Cascadic Multigrid Method for Cell-Centered FV Discretization of Diffusion Equations with Strongly Discontinuous and Anisotropic Coefficients. Communications in Computational Physics, 2022, 31(5): 1561-1584.
[20]. Guo R, Wang Y, Egbert G D, Liu J, Liu R, Pan K, et al. An efficient multigrid solver based on a four-color cell-block Gauss-Seidel smoother for 3D magnetotelluric forward modeling. Geophysics, 2022, 87(3): E121-E133.
[21]. Wu X, Pan K*, Li J, Yu Y, Yuan G, Ren Z. A robust, interpolation-free and monotone finite volume scheme for diffusion equations on arbitrary quadrilateral meshes. International Journal for Numerical Methods in Engineering, 2022, 123: 3631-3657.（封面论文）
[22]. Chen R, Li Y, Pan K, Yang X. Efficient second-order, linear, decoupled and unconditionally energy stable schemes of the Cahn-Hilliard-Darcy equations for the Hele-Shaw flow. Numerical Algorithms, 2022, 1-32.
[23]. Ali R, Pan K, Two new fixed point iterative schemes for absolute value equations. Japan Journal of Industrial and Applied Mathematics, 2022: 1-12.
[24]. Wu P, Pan K*, Ling W, Wu Q. A linearly implicit scheme and fast multigrid solver for 3D Fitzhugh-Nagumo equation, Computers & Mathematics with Applications , 2022, 117: 257-270.
[25]. Ali R, Pan K, Ali A. Two new iteration methods with optimal parameters for solving absolute value equations. International Journal of Applied and Computational Mathematics, 2022, 8(3): 123.
[26]. Shah MA, Pan K*, Ibrahim M, Saeed T. Use of neural network and machine learning in optimizing heat transfer and entropy generated in a cavity filled with nanofluid under the influence of magnetic field: A numerical study. Engineering Analysis with Boundary Elements, 2022, 139: 113-131.
[27]. Shah MA, Pan K*, Ibrahim M, Saeed T, Ibrahim S. Numerical study and optimization of important parameters of non-Newtonian nanofluid turbulent flow in a channel with triangular vortex generators using artificial neural network. Engineering Analysis with Boundary Elements, 2022, 139: 94-108.
[28]. Pan K, Zeng J, He D, Zhang S. A fourth-order difference scheme for the fractional nonlinear Schrödinger equation with wave operator. Applicable Analysis, 2022, 101(8):2886-2902.
[29]. Wang J, Pan K, Yang X. Convergence Analysis of the Fully Discrete Hybridizable Discontinuous Galerkin Method for the Allen–Cahn Equation Based on the Invariant Energy Quadratization Approach. Journal of Scientific Computing, 2022, 91 (2): 49.
[30]. Hu H, Li M, Pan K, Wu P. An extrapolation accelerated multiscale Newton-MG method for fourth-order compact discretizations of semilinear Poisson equations. Computers & Mathematics with Applications, 2022, 113: 189-197.
[31]. Ali R, Pan K. The solution of the absolute value equations using two generalized accelerated overrelaxation methods. Asian-European Journal of Mathematics, 2022, 2250154.
[32]. Ali R, Pan K. The solution of a type of absolute value equations using two new matrix splitting iterative techniques, Portugaliae Mathematica, 2022, 79 (3/4): 241-252.
[33]. Hu H, Jin X, He D, Pan K, Zhang Q. A conservative difference scheme with optimal pointwise error estimates for two-dimensional space fractional nonlinear Schrödinger equations. Numerical Methods for Partial Differential Equations, 2022, 38(1): 4-32.
2021年
[34]. Pan K, Zhang Z, Hu S, Ren Z, Guo R, Tang J. Three-dimensional forward modeling of gravity field vector and its gradient tensor using the compact difference schemes. Geophysical Journal International, 2021, 224(2): 1272–1286.
[35]. Pan K, He D, Li Z. A high order compact FD framework for elliptic BVPs involving singular sources, interfaces, and irregular domains. Journal of Scientific Computing, 2021, 88(3): 67.
[36]. Pan K, Sun HW, Xu Y, Xu Y. An efficient multigrid solver for two-dimensional spatial fractional diffusion equations with variable coefficients. Applied Mathematics and Computation, 2021, 402, 126091.
[37]. K Naseer M, B Habib Ben, Pan K*, Tareq S. Nonlinear Eyring–Powell bioconvective nanofluid flow over a vertical plate with temperature dependent viscosity and surface suction. International Communications in Heat and Mass Transfer, 2021, 128, 105602.
[38]. Deng S, Li Z, Pan K. An ADI-Yee's scheme for Maxwell's equations with discontinuous coefficients. Journal of Computational Physics, 2021, 438, 110356.
[39]. Hu H, Chen C, Hu S, Pan K. Superconvergence of the space-time discontinuous Galerkin method for linear nonhomogeneous hyperbolic equations. Calcolo, 2021, 58 (2):16.
[40]. Yue X, Pan K, Zhou J, Weng Z, Shu S, Tang J. A multigrid-reduction-in-time solver with a new two-level convergence for unsteady fractional Laplacian problems. Computers & Mathematics with Applications, 2021, 89: 57-67.
[41]. Pan M, Wang Q, He D, Pan K. Positive-definiteness preserving and energy stable time-marching scheme for a diffusive Oldroyd-B electrohydrodynamic model. Communications in Nonlinear Science and Numerical Simulation, 2021, 95: 105630.
[42]. Li X, Li T, Tu R, Pan K, Chen C, Yang X. Efficient energy stable scheme for volume-conserved phase-field elastic bending energy model of lipid vesicles. Journal of Computational and Applied Mathematics, 2021, 385: 113177.
[43]. Pan M, He D, Pan K. Energy stable finite element method for an electrohydrodynamic model with variable density. Journal of Computational Physics, 2021, 424: 109870.
[44]. Li M, Zheng Z, Pan K*. An efficient extrapolation full multigrid method for elliptic problems in two and three dimensions. International Journal of Computer Mathematics, 2021, 98 (6): 1183–1198.
2020年
[45]. Pan K, Xia J, He D, Zhang Q. A three-level linearized difference scheme for nonlinear Schrödinger equation with absorbing boundary conditions. Applied Numerical Mathematics, 2020, 156: 32-49.
[46]. Pan K, Jin X, He D. Pointwise error estimates of a linearized difference scheme for strongly coupled fractional Ginzburg‐Landau equations. Mathematical Methods in the Applied Sciences, 2020, 43(2): 512-535.
[47]. Zhang Q*, Lin X, Pan K*, Ren Y. Linearized ADI schemes for two-dimensional space-fractional nonlinear Ginzburg–Landau equation. Computers & Mathematics with Applications, 2020, 80(5): 1201-1220.（高被引论文）
[48]. Chen C, Pan K, Yang X. Numerical approximations of a hydro-dynamically coupled phase-field model for binary Mixture of passive/active nematic Liquid Crystals and Viscous Fluids. Applied Numerical Mathematics, 2020, 58: 1-21.
[49]. Khan MR, Pan K, Khan AU, Ullah N. Comparative study on heat transfer in CNTs-water nanofluid over a curved surface. International Communications in Heat and Mass Transfer, 2020, 116: 104707.
[50]. Li M, Zheng Z, Pan K*, Yue X. An Efficient Newton Multiscale Multigrid Method for 2D Semilinear Poisson Equations. East Asian Journal on Applied Mathematics, 2020, 10: 620-634.
[51]. Khan MR, Pan K, Khan AU, Nadeem S. Dual solutions for mixed convection flow of SiO2− Al2O3/water hybrid nanofluid near the stagnation point over a curved surface. Physica A: Statistical Mechanics and its Applications, 2020, 547: 123959. （热点论文）
[52]. Zhang J, Chen C, Yang X, Pan K. Efficient numerical scheme for a penalized Allen-Cahn type Ohta-Kawasaki phase-field model for diblock copolymers. Journal of Computational and Applied Mathematics, 2020, 378: 112905.
[53]. Pan M, He D, Pan K. Unconditionally energy stable schemes for an electrohydrodynamic model of charge transport in dielectric liquids. Computer Methods in Applied Mechanics and Engineering, 2020, 361: 112817.
[54]. He D, Pan K, Hu H. A spatial fourth-order maximum principle preserving operator splitting scheme for the multi-dimensional fractional Allen-Cahn equation. Applied Numerical Mathematics, 2020, 151: 44-63.
[55]. Li J, Liu J, Egbert GD, Liu R, Guo R, Pan K. An efficient preconditioner for 3-D finite difference modeling of the electromagnetic diffusion process in the frequency domain. IEEE Transactions on Geoscience and Remote Sensing, 2022, 58(1): 500-509.
[56]. Pan K, Wu X, Yue X, Ni R. A spatial sixth-order CCD-TVD method for solving multidimensional coupled Burgers' equation. Computational and Applied Mathematics, 2020, 39(2).
2019年
[57]. Liu J, Pan K, Wu J. A class of large solutions to the supercritical surface quasi-geostrophic equation. Nonlinearity, 2019, 32(12): 5049-5059.
[58]. He D, Pan K*. Maximum norm error analysis of an unconditionally stable semi-implicit scheme for multi-dimensional Allen-Cahn equations. Numerical Methods for Partial Differential Equations, 2019, 35(3): 955-975.
[59]. He D, Pan K*, Yue X. A positivity preserving and free energy dissipative difference scheme for the Poisson–Nernst–Planck system. Journal of Scientific Computing, 2019, 81(1): 436-458.
[60]. Cai W, He D, Pan K. A linearized energy–conservative finite element method for the nonlinear Schrödinger equation with wave operator. Applied Numerical Mathematics, 2019, 140: 183-198.
[61]. Li M, Zheng Z, Pan K*. Extrapolation multiscale multigrid method for solving 2D Poisson equation with sixth order compact scheme. Journal of Applied Mathematics and Computing, 2019, 60(1-2): 589-604.
[62]. Chen B, He D, Pan K. A CCD-ADI method for two-dimensional linear and nonlinear hyperbolic telegraph equations with variable coefficients. International Journal of Computer Mathematics, 2019, 96(5): 992–1004. （高被引论文）
[63]. Yue X, Shu S, Xu X, Bu W, Pan K*. Parallel-in-time multigrid for space-time finite element approximations of two-dimensional space-fractional diffusion equations. Computer and Mathematics with Applications, 2019, 78(11): 3471-3484.
2018年
[64]. He D, Pan K*. An unconditionally stable linearized difference scheme for the fractional Ginzburg-Landau equation. Numerical Algorithms, 2018, 79(3): 899-925.
[65]. Chen C, Ren Z, Pan K, Tang J, T Kalscheuer, H Maurer, Y Sun, Y Li. Exact solutions of the vertical gravitational anomaly for a polyhedral prism with vertical polynomial density contrast of arbitrary orders. Geophysical Journal International, 2018, 214 (3): 2115–2132.
[66]. Pan Q, Rabczuk T, Chen C, Xu G, Pan K. Isogeometric analysis of minimal surfaces on the basis of extended Catmull-Clark subdivision. Computer Methods in Applied Mechanics and Engineering, 2018, 337: 128-149.
[67]. Chen B, He D, Pan K. A Linearized High-Order Combined Compact Difference Scheme for Multi-Dimensional Coupled Burgers’ Equations. Numerical Mathematics-Theory Methods and Applications, 2018, 11 (2): 299-320.
[68]. He D, Pan K. A fifth-order combined compact difference scheme for the Stokes flow on polar geometries. East Asian Journal on Applied Mathematics, 2018, 7 (4): 714-727.
[69]. Ren Z, Zhong Y, Chen C, Tang J, Pan K. Gravity anomalies of arbitrary 3D polyhedral bodies with horizontal and vertical mass contrasts up to cubic order. Geophysics, 2018, 83 (1): G1-G13.（高被引论文）
2017年
[70]. Pan K, He D, Hu H, Ren Z. A new extrapolation cascadic multigrid method for three dimensional elliptic boundary value problems. Journal of Computational Physics, 2017, 344: 499-515.
[71]. Pan K, He D, Hu H. An extrapolation cascadic multigrid method combined with a fourth order compact scheme for 3D poisson equation. Journal of Scientific Computing, 2017, 70(3): 1180-1203.
[72]. Ren Z, Chen C, Pan K*, Kalscheuer T, Maurer H, Tang J. Gravity anomalies of arbitrary 3D polyhedral bodies with horizontal and vertical mass contrasts. Surveys in geophysics, 2017, 38(2): 479-502.（热点论文）
[73]. Pan K, He D, Chen C. An extrapolation cascadic multigrid method for elliptic problems on reentrant domains. Advances in Applied Mathematics and Mechanics, 2017, 9 (6): 1347-1363.
[74]. Hu H, Ren Z, He D, Pan K*. On the convergence of an extrapolation cascadic multigrid method for elliptic problems. Computers & Mathematics with Applications, 2017, 74 (4): 759-771.
[75]. He D, Pan K*. An unconditionally stable linearized CCD–ADI method for generalized nonlinear Schrödinger equations with variable coefficients in two and three dimensions. Computers & Mathematics with Applications, 2017, 73 (11): 2360-2374.
[76]. 李龙艳, 曹扬, 潘克家. 基于差分进化算法优化多因素灰色模型的异丙酚血药浓度预测. 药学学报, 2017, 52(10): 1599-1604.
2016年
[77]. 潘克家, 汤井田, 杜华坤, 蔡志杰. 轴对称地层中高分辨率阵列侧向测井信赖域反演法. 地球物理学报, 2016, 59 (8): 3110-3120.
[78]. Klibanov MV, Nguyen LH, Pan K*. Nanostructures imaging via numerical solution of a 3-d inverse scattering problem without the phase information. Applied Numerical Mathematics, 2016, 110: 190-203.
[79]. He D, Pan K*. An energy preserving finite difference scheme for the Poisson–Nernst–Planck system. Applied Mathematics and Computation, 2016, 287: 214-223.
2015年
[80]. He D, Pan K*. An order optimal regularization method for the Cauchy problem of a Laplace equation in an annulus domain. Applied Mathematical Modelling, 2015, 39(10-11), 3063–3074.
[81]. He D, Pan K. A linearly implicit conservative difference scheme for the generalized Rosenau-Kawahara-RLW equation. Applied Mathematics and Computation, 2015, 271: 323-336.
2014年
[82]. Pan K, Tang J. 2.5-D and 3-D DC resistivity modelling using an extrapolation cascadic multigrid method. Geophysical Journal International, 2014, 197(3): 1459-1470.
[83]. Pan K, Liu J. A parameter identification problem for spontaneous potential logging in heterogeneous formation. Journal of Inverse and Ill-posed Problems, 2014, 22(3): 357-373.
[84]. Hu H, Chen C, Pan K. Asymptotic expansions of finite element solutions to Robin problems in H 3 and their application in extrapolation cascadic multigrid method. Science China Mathematics, 2014, 57(4): 687-698.
[85]. Hu H, Chen C, Pan K. Time-extrapolation algorithm (TEA) for linear parabolic problems. Journal of Computational Mathematics, 2014, 32(2): 183-194.
[86]. 胡宏伶, 肖晓, 潘克家, 汤井田, 谢维. 基于局部加密等级网格的 2.5 D 直流电法有限元模拟. 中南大学学报 (自然科学版), 2014, 45(7): 2259-2267.
[87]. 汤井田, 谭洁, 潘克家. 垂直及倾斜接触面电测深曲线特征. 物探化探计算技术, 2014, 36(1): 1-8.
2013年
[88]. 潘克家, 王文娟, 汤井田, 谭永基. 高分辨率阵列侧向测井的数学模型及有限元快速正演. 地球物理学报, 2013, 56(9): 3197-3211.
[89]. 潘克家, 汤井田. 2.5维直流电法正演中Fourier逆变换离散波数的最优化选取. 中南大学学报自然科学版, 2013, 44(7): 2819-2826.
[90]. 潘克家, 汤井田. 单纯形上校正高斯-勒让德求积公式. 计算机工程与应用, 2012, 48 (35): 7-10.
[91]. 胡宏伶, 潘克家. 基于 CG 的外推瀑布式多网格法收敛性分析. 高等学校计算数学学报, 2013, 35(4): 340-351.
2012年
[92]. 潘克家, 汤井田, 胡宏伶, 陈传淼. 直流电阻率法2.5维正演的外推瀑布式多重网格法. 地球物理学报, 2012, 55(8): 2769-2778.
[93]. 潘克家, 胡宏伶, 陈传淼, 汤井田. 外推瀑布式多网格法的OpenMP并行化. 计算数学, 34(4): 425-436.
[94]. 潘克家, 刘见礼, 甘四清. 高斯型数值求积公式的校正. 数值计算与计算机应用, 33 (1): 17-24.
[95]. Liu J, Pan K*. Asymptotic behavior of global classical solutions to Goursat problem of quasilinear hyperbolic systems. Journal of Mathematical Analysis and Applications, 392(2): 200-208.
[96]. Liu J, Pan K*. Global existence and asymptotic behavior of classical solutions to Goursat problem for diagonalizable quasilinear hyperbolic system. Boundary Value Problems, 2012, (1): 1-13.
2011年及以前
[97]. Pan K, Tan Y, Hu H. An interpolation matched interface and boundary method for elliptic interface problems. Journal of computational and applied mathematics, 234(1): 73-94.
[98]. Pan K, Tan Y, Hu H. Mathematical model and numerical method for spontaneous potential log in heterogeneous formations. Applied Mathematics and Mechanics, 2009, 30(2), 209-219.
[99]. 潘克家, 王文娟, 谭永基, 曹俊兴. 基于混合差分进化算法的地球物理线性反演. 地球物理学报, 2009, 52(12): 3083-3090.
[100]. 潘克家, 陈华, 谭永基. 基于差分进化算法的核磁共振 T2 谱多指数反演. 物理学报, 2008, 57(9), 5956-5961.
[101]. 潘克家, 谭永基. 复杂地层中自然电位测井的高效数值模拟. 石油地球物理勘探, 2009, 44(3):371-376.
[102]. 潘克家, 谭永基, 王才经. 自动识别油藏边界水侵量微分方程反演算法. 石油学报, 2008, 29(5):747-751.
[103]. 潘克家, 汤井田, 郑洲顺. Matlab与Fortran 混合编程之DLL实现方法. 计算机工程与应用, 2011, 47(31):1-3.
[104]. 王文娟, 潘克家, 曹俊兴, 谭永基. 基于 Tikhonov 正则化的双频电磁波电导率成像反演. 地球物理学报, 2009, 52(3): 750-757.
[105]. 王文娟, 谢滨, 潘克家, 王景婷, 冯宝宾. 利用加速差分进化算法反演非均匀介质电磁成像. 地球物理学进展, 2010: 2002-2008.
[106]. Li C, Pan K. A Jump Condition Capturing Finite Difference Scheme for Spontaneous Potential Log. 湖南师范大学自然科学学报, 2010, 33(1):17-22.
[107]. Wang W, Pan K*, Cao J. Conductivity tomography imaging using regularization methods. Journal of Information and Computation Science, 2008, 5(4): 1885-1891.
[108]. 陈华, 潘克家, 谭永基. 核磁共振弛豫信号多指数反演新方法. 测井技术, 2009, 33(1): 37-41.