{"id":86,"date":"2021-11-11T18:16:41","date_gmt":"2021-11-11T18:16:41","guid":{"rendered":"https:\/\/dev-cu-sites.pantheonsite.io\/brian-helenbrook\/?page_id=86"},"modified":"2025-11-10T19:18:23","modified_gmt":"2025-11-10T19:18:23","slug":"articles","status":"publish","type":"page","link":"https:\/\/sites.clarkson.edu\/brian-helenbrook\/publications\/articles\/","title":{"rendered":"Articles"},"content":{"rendered":"\n

Articles <\/h2>\n\n\n\n

2021<\/h3>\n\n\n\n
    \n
  1. J. Appleton and B. T. Helenbrook Mass-lumping for triangular hp-finite elements part I: Nonexistence of an accurate diagonal scheme SIAM J. Num. Analysis, submitted.<\/li>\n\n\n\n
  2. L. M. D\u2019Aquila, B. T. Helenbrook, A. Mazaheri A novel stabilization method for high-order shock fitting with finite element methods. Journal of Computational Physics 430: 110096, 2021. DOI: https:\/\/doi.org\/10.1016\/j.jcp.2020.110096<\/a><\/li>\n\n\n\n
  3. A. Pirnia and B. T. Helenbrook Analysis of faceted solidification in the horizontal ribbon growth crystallization process. J. of Crystal Growth 555:125958, 2021. DOI: https:\/\/doi.org\/10.1016\/j.jcrysgro.2020.125958<\/a><\/li>\n\n\n\n
  4. N. Bagheri-Sadeghi, B. T. Helenbrook, and K. D. Visser. Maximal power per device area of a ducted turbine. Wind Energy Science Discussions, pages 1\u201316, 2021. DOI: http:\/\/dx.doi.org\/10.5194\/wes-6-1031-2021<\/a><\/li>\n\n\n\n
  5. J. M. Appleton and B. T. Helenbrook. A high-order lower-triangular pseudo-mass matrix for explicit time advancement of hp triangular finite element methods. SIAM Journal on Numerical Analysis, 59(3):1618\u20131638, 2021. DOI: https:\/\/doi.org\/10.1137\/19M1268471<\/a><\/li>\n<\/ol>\n\n\n\n

    2020<\/h3>\n\n\n\n
      \n
    1. A. Pirnia, J. McClure, S. Peterson, B. T. Helenbrook, and B. Erath. Estimating pressure fields from planar velocity data around immersed bodies; a finite element approach. Experiments in Fluids, 61(2):1\u201316, 2020. DOI: https:\/\/doi.org\/10.1007\/s00348-020-2886-z<\/a><\/li>\n<\/ol>\n\n\n\n

      2019<\/h3>\n\n\n\n
        \n
      1. F. Hejripour, B. T. Helenbrook, D. Valentine, and D. Aidun. Mass transport and solidification phenomenon in dissimilar metals arc welding. Int. J. of Heat and Mass Transfer, 144:118703, 2019. DOI: https:\/\/doi.org\/10.1016\/j.ijheatmasstransfer.2019.118703<\/a><\/li>\n\n\n\n
      2. A.M. Bluestein, R. Venters, D. Bohl, B. T. Helenbrook and G. Ahmadi. Turbulent flow through a ducted elbow and plugged tee geometry: An experimental and numerical study. ASME J. of Fluids Eng., 141(8):081101, 2019. DOI:  https:\/\/doi.org\/10.1115\/1.4042256<\/a><\/li>\n<\/ol>\n\n\n\n

        2018<\/h3>\n\n\n\n
          \n
        1. I. Udagedara, B. T. Helenbrook, A. Luttman, and J. Catenacci. Probabilistic reduced order modeling. American Journal of Mathematics and Sciences, 3(2):50\u201361, 2018. <\/li>\n\n\n\n
        2. B. T. Helenbrook and D. ben Avraham. Ordering statistics of four random walkers on a line. Phys. Rev. E, 97:052105, May 2018. DOI: https:\/\/doi.org\/10.1103\/PhysRevE.97.052105<\/a><\/li>\n\n\n\n
        3. N. Bagheri-Sadeghi, B. T. Helenbrook, and K. D. Visser Ducted wind turbine optimization and sensitivity to rotor position Wing Energy Science, 3(1):221-229, 2018. DOI: https:\/\/doi.org\/10.5194\/wes-3-221-2018<\/a><\/li>\n\n\n\n
        4. F. Behzad, B. T. Helenbrook, and G. Ahmadi. The multi-level proper orthogonal decomposition. AIAA Journal, 56(11):4423-4436, 2018. <\/li>\n\n\n\n
        5. B. T. Helenbrook and J. Hrdina high-order adaptive arbitrary-lagrangian-Eulerian (ALE) simulations of solidification Computers & Fluids, 167:40-50, 2018. DOI: https:\/\/doi.org\/10.1016\/j.compfluid.2018.02.028<\/a><\/li>\n\n\n\n
        6. R. Venters, B. T. Helenbrook, and K. D. Visser. Ducted wind-turbine optimization J. Solar Energy Eng., 140(1):011005, 2018. DOI: https:\/\/doi.org\/10.1115\/1.4037741<\/a><\/li>\n<\/ol>\n\n\n\n

          2017<\/h3>\n\n\n\n
            \n
          1. D. S. Meyer, B. T. Helenbrook, and M.-C. Cheng. Proper orthagonal decomposition-based reduced basis element method for thermal modeling of intergrated circuits. Int. J. Num. Meth. Eng., 112(5):479-500, 2017. <\/li>\n\n\n\n
          2. N. S. Barlow, B. T. Helenbrook, and S. J. Weingstein. Algorithm for Spatio-Temporal Analysis of the Signalling Problem. IMA Journal of Applied Mathematics, 82(1):1-32, 2017. DOI: https:\/\/doi.org\/10.1093\/imamat\/hxv040<\/a><\/li>\n<\/ol>\n\n\n\n

            2016<\/h3>\n\n\n\n
              \n
            1. B. T. Helenbrook and N. S. Barlow. 2016 Spatial-temporal stability analysis of faceted growth with application to horizontal ribbon growth. Journal of Crystal Growth, 454:35\u201344, 2016. DOI: https:\/\/doi.org\/10.1016\/j.jcrysgro.2016.08.052<\/a><\/li>\n\n\n\n
            2. B. T. Helenbrook, P. Kellerman, F. Carlson, N. Desai, and D. Sun. Experimental and numerical investigation of the horizontal ribbon growth process. Journal of Crystal Growth, 453:163\u2013172, 2016. DOI: https:\/\/doi.org\/10.1016\/j.jcrysgro.2016.08.034<\/a><\/li>\n\n\n\n
            3. P. Kellerman, B. Kernan, B. T. Helenbrook, D. Sun, F. Sinclair, and F. Carlson. Floating Silicon Method single crystal ribbon\u2013observations and proposed limit cycle theory. Journal of Crystal Growth, 451:174\u2013180, 2016. DOI: https:\/\/doi.org\/10.1016\/j.jcrysgro.2016.07.012<\/a><\/li>\n\n\n\n
            4. A. Bahrami, and D. T. Valentine, B. T. Helenbrook, and D. K. Aidun. Fluid flow and mixing in linear GTA welding of dissimilar ferrous alloys. International Journal of Heat and Mass Transfer, 93:729\u2013741, 2016. DOI: https:\/\/doi.org\/10.1016\/j.ijheatmasstransfer.2015.10.058<\/a><\/li>\n<\/ol>\n\n\n\n

              2015<\/h3>\n\n\n\n
                \n
              1. I. Udagedara, B. T. Helenbrook, A. Luttman, and S. Mitchell. Reduced order modeling for accelerated Monte Carlo simulations in radiation transport. Appl. Math. Computation., 267:237\u2013251, 2015. DOI: https:\/\/doi.org\/10.1016\/j.amc.2015.03.113<\/a><\/li>\n\n\n\n
              2. B. T. Helenbrook Solidification along a wall or free surface with heat removal. J. Crystal Growth, 418:79\u201385, 2015. DOI: https:\/\/doi.org\/10.1016\/j.jcrysgro.2015.02.028<\/a><\/li>\n\n\n\n
              3. K. Perline and B. T. Helenbrook. A hybrid level-set\/moving-mesh interface tracking method. Applied Num. Mathematics, 92:21\u201339, 2015. DOI: https:\/\/doi.org\/10.1016\/j.apnum.2015.01.004<\/a><\/li>\n\n\n\n
              4. A. Bahrami, and D. Valentine, B. T. Helenbrook, and D. K. Aidun. Study of mass transport in autogenous GTA welding of dissimilar metals Int. J. Heat and Mass Transfer, 85:41\u201353, 2015. DOI: https:\/\/doi.org\/10.1016\/j.ijheatmasstransfer.2015.01.074<\/a><\/li>\n\n\n\n
              5. F. Behzad, B. T. Helenbrook, and G. Ahmadi. On the sensitivity and accuracy of proper-orthogonal-decomposition-based reduced order models for Burger\u2019s equation. Comp. & Fluids, 106:19\u201332, 2015. DOI: https:\/\/doi.org\/10.1016\/j.compfluid.2014.09.041<\/a><\/li>\n\n\n\n
              6. W. Jia, B. T. Helenbrook, and M.-C. Cheng. Fast thermal simulation of FinFET circuits based on a multi-block reduced-order model. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 35(7):1114\u20131124, July 2015. DOI: 10.1109\/TCAD.2015.2501305<\/a><\/li>\n<\/ol>\n\n\n\n

                2014<\/h3>\n\n\n\n
                  \n
                1. W. Jia, M.-C. Cheng, and B. T. Helenbrook. Thermal modeling of multi-fin field effect transistor structure using proper orthogonal decomposition. IEEE Trans. Electron Devices, 61(8):2752\u20132759, 2014. DOI: 10.1109\/TED.2014.2332414<\/a><\/li>\n<\/ol>\n\n\n\n

                  2013<\/h3>\n\n\n\n
                    \n
                  1. M. J. Brazell and B. T. Helenbrook. Continuous finite elements on tetrahedral with local mass matrix inversion to solve the preconditioned compressible Navier-Stokes equations. Computers & Fluids, 88:643\u2013652, 2013. DOI: https:\/\/doi.org\/10.1016\/j.compfluid.2013.10.025<\/a><\/li>\n<\/ol>\n\n\n\n

                    2012<\/h3>\n\n\n\n
                      \n
                    1. R. Venters, B. T. Helenbrook, K. Zhang, and M.-C. Cheng. Proper orthogonal decomposition based thermal modeling of semiconductor structures. IEEE Transactions on Electron Devices, 59(11):2924\u20132931, 2012. DOI: 10.1109\/TED.2012.2211878<\/a><\/li>\n\n\n\n
                    2. P. Zamankhan, B. T. Helenbrook, S. Takayama, and J. Grotberg. Steady motion of Bingham plugs in 2D channels. J. Fluid Mech., 705:258\u2013279, 2012. DOI: https:\/\/doi.org\/10.1017\/jfm.2011.438<\/a><\/li>\n\n\n\n
                    3. N. S. Barlow, S. J. Weinstein, and B. T. Helenbrook. On the response of convectively unstable flows to oscillatory forcing with application to liquid sheets. J. Fluid Mech., 699:115\u2013152, 2012. DOI: https:\/\/doi.org\/10.1017\/jfm.2012.86<\/a><\/li>\n\n\n\n
                    4. M. J. Brazell and B. T. Helenbrook. p=2 continuous finite elements on tetrahedra with local mass matrix inversion. Computer Methods in Applied Mechanics and Engineering, 213\u2013216(0):289\u2013298, 2012. DOI: https:\/\/doi.org\/10.1016\/j.cma.2011.12.001<\/a><\/li>\n<\/ol>\n\n\n\n

                      2011<\/h3>\n\n\n\n
                        \n
                      1. M. A. Karri, B. T. Helenbrook, and E. F. Thacher. Exhaust energy conversion by thermoelectric generation: Two case studies. Energy Conversion and Management, 52(3):1596\u20131611, 2011. DOI: https:\/\/doi.org\/10.1016\/j.enconman.2010.10.013<\/a><\/li>\n\n\n\n
                      2. N. S. Barlow, B. T. Helenbrook, and S. P. Lin. Transience to instability in a liquid sheet. J. Fluid Mech., 666:358\u2013390, 2011. DOI:  https:\/\/doi.org\/10.1017\/S0022112010004416<\/a><\/li>\n<\/ol>\n\n\n\n

                        2010<\/h3>\n\n\n\n
                          \n
                        1. N. S. Barlow, B. T. Helenbrook, S. P. Lin, and S. J. Weinstein. An interpretation of absolutely and convectively unstable waves using series solutions. Wave Motion, 47:564-582, 2010. DOI: https:\/\/doi.org\/10.1016\/j.wavemoti.2010.04.003<\/a><\/li>\n\n\n\n
                        2. B. Mascarenhas, B. T. Helenbrook, and H. L. Atkins. Coupling p-multigrid to geometric multigrid for discontinuous Galerkin solutions of the wave equation. J. Comp. Phys., 229:3664-3674, 2010. DOI: https:\/\/doi.org\/10.1016\/j.jcp.2010.01.020<\/a><\/li>\n<\/ol>\n\n\n\n

                          2009<\/h3>\n\n\n\n
                            \n
                          1. Q. Zhou, H. H. Shen, B. T. Helenbrook, and H. W. Zhang. ‘High order finite element model for core loss assessment in a hysteresis magnetic lamination. J. Applied Physics, 106(4), 2009. DOI: https:\/\/doi.org\/10.1063\/1.3176492<\/a><\/li>\n\n\n\n
                          2. N. S. Barlow, B. T. Helenbrook, and S. P. Lin. A numerical investigation of the stability of expanding liquid sheets and the influence of boundary conditions. Comput. & Fluids, 38(3):552-563, 2009. DOI: https:\/\/doi.org\/10.1016\/j.compfluid.2008.05.005<\/a><\/li>\n\n\n\n
                          3. B. T. Helenbrook. On the existence of explicit hp-finite element methods using Gauss\u2013Lobatto integration on the triangle SIAM J. Numer. Anal., 47(2):1304\u20131318, 2009.<\/li>\n\n\n\n
                          4. B. Mascarenhas, B. T. Helenbrook, and H. L. Atkins. Application of pmultigrid to discontinuous Galerkin formulations of the Euler equations. AIAA Journal, 47(5):1200\u20131208, 2009.<\/li>\n\n\n\n
                          5. B. T. Helenbrook, H. H. Shen, M. P. Powers, and P. T. Metzger. Continuum modeling and discrete element simulations of elastic-quasi-static granular flow in a compressing slot. Journal of Aerospace Engineering, 22(4):415\u2013422, 2009. DOI: https:\/\/ascelibrary.org\/doi\/full\/10.1061\/%28ASCE%290893-1321%282009%2922%3A4%28415%29<\/a><\/li>\n\n\n\n
                          6. Q. Zhou, H. H. Shen, B. T. Helenbrook, and H. Wu, Scale dependence of direct shear tests. Chinese Science Bulletin 54:4337\u20134348, 2009.<\/li>\n<\/ol>\n\n\n\n

                            2008<\/h3>\n\n\n\n
                              \n
                            1. B. T. Helenbrook and G. W. Cowles. Preconditioning for dual-time-stepping simulations of the shallow water equations including coriolis effects. J. Comp. Phys., 227(9):4425\u20134440, 2008. DOI: https:\/\/doi.org\/10.1016\/j.jcp.2008.01.004<\/a><\/li>\n\n\n\n
                            2. B. T. Helenbrook and H. L. Atkins. Solving discontinuous Galerkin formulations of Poisson\u2019s equation using geometric and p-multigrid. AIAA Journal, 46(4):894\u2013902, 2008. DOI: https:\/\/doi.org\/10.2514\/1.31163<\/a><\/li>\n<\/ol>\n\n\n\n

                              2007<\/h3>\n\n\n\n
                                \n
                              1. B. J. O\u2019Donnell and B. T. Helenbrook. Proper orthogonal decomposition and incompressible flow: An application to particle modeling. Comput. & Fluids, 36(7):1174\u20131186, August 2007. DOI: https:\/\/doi.org\/10.1016\/j.compfluid.2006.12.004<\/a><\/li>\n\n\n\n
                              2. E. F. Thacher, B. T. Helenbrook, M. A. Karri, and C. J. Richter. Testing an automobile exhaust thermoelectric generator in a light truck. Proc. IMechE, Part D: J. Automobile Engineering, 221(D1):95\u2013107, 2007. DOI: https:\/\/doi.org\/10.1243\/09544070JAUTO51<\/a><\/li>\n<\/ol>\n\n\n\n

                                2006<\/h3>\n\n\n\n
                                  \n
                                1. B. T. Helenbrook and H. L. Atkins. Application of \u201cp\u201d-multigrid to discontinuous Galerkin formulations of the Poisson equation. AIAA Journal, 44(3):566\u2013575, March 2006. DOI: https:\/\/doi.org\/10.2514\/1.15497<\/a><\/li>\n<\/ol>\n\n\n\n

                                  2005<\/h3>\n\n\n\n
                                    \n
                                  1. B. T. Helenbrook. Preconditioning for incompressible flows with freesurfaces and two-fluid interfaces. J. Comp. Phys., 207(1):282\u2013308, 2005. DOI: https:\/\/doi.org\/10.1016\/j.jcp.2005.01.012<\/a><\/li>\n\n\n\n
                                  2. W. Y. Jiang, S. J. Weinstein, B. T. Helenbrook, and S. P. Lin. Low Reynolds number instabilities in three-layer flow down an inclined wall. J. Fluid Mech., 539:387\u2013416, 2005. DOI: https:\/\/doi.org\/10.1017\/S0022112005005781<\/a><\/li>\n\n\n\n
                                  3. B. J. O\u2019Donnell and B. T. Helenbrook. Drag on ellipsoids at finite Reynolds numbers. Atomization and Sprays, 15(4):363\u2013376, 2005.<\/li>\n<\/ol>\n\n\n\n

                                    2004<\/h3>\n\n\n\n
                                      \n
                                    1. W. Y. Jiang, B. T. Helenbrook, and S. P. Lin. Inertialess instability of a twolayer liquid film flow. Phys. Fluids, 16(3):652\u2013663, March 2004. DOI: https:\/\/doi.org\/10.1063\/1.1642657<\/a><\/li>\n<\/ol>\n\n\n\n

                                      2003<\/h3>\n\n\n\n
                                        \n
                                      1. B. T. Helenbrook. Mesh deformation using the biharmonic operator. Int. J. Num. Meth. Eng., 56(7):1007\u20131021, 2003. DOI: https:\/\/doi.org\/10.1002\/nme.595<\/a><\/li>\n<\/ol>\n\n\n\n

                                        2002<\/h3>\n\n\n\n
                                          \n
                                        1. B. T. Helenbrook and C. F. Edwards. Quasi-steady deformation and drag of uncontaminated liquid drops. Int. J. Multi-Phase Flows., 28:1631\u20131657, 2002. DOI: https:\/\/doi.org\/10.1016\/S0301-9322(02)00073-3<\/a><\/li>\n<\/ol>\n\n\n\n

                                          2001<\/h3>\n\n\n\n
                                            \n
                                          1. B. T. Helenbrook. A two-fluid spectral element method. Comp. Meth. Appl. Mech. Eng., 191(3\u20135):273\u2013294, November 2001. DOI: https:\/\/doi.org\/10.1016\/S0045-7825(01)00275-4<\/a><\/li>\n<\/ol>\n\n\n\n

                                            1999<\/h3>\n\n\n\n
                                              \n
                                            1. B. T. Helenbrook and C. K. Law. The role of Landau-Darrieus instability in large scale flows. Comb. Flame, 117:155\u2013169, 1999.<\/li>\n\n\n\n
                                            2. B. T. Helenbrook, L. Martinelli, and C. K. Law. A numerical method for solving incompressible flow problems with a surface of discontinuity. J. Comp. Phys., 148:366\u2013396, 1999. DOI: https:\/\/doi.org\/10.1006\/jcph.1998.6115<\/a><\/li>\n<\/ol>\n\n\n\n

                                              1998<\/h3>\n\n\n\n
                                                \n
                                              1. B. T. Helenbrook, H. G. Im, and C. K. Law. Theory of radical-induced ignition of counterflowing hydrogen versus oxygen at high temperatures. Combustion and Flame, 112:242\u2013252, 1998. DOI: https:\/\/doi.org\/10.1016\/S0010-2180(97)81772-5<\/a><\/li>\n<\/ol>\n\n\n\n

                                                1996<\/h3>\n\n\n\n
                                                  \n
                                                1. H. G. Im, B. T. Helenbrook, S. R. Lee, and C. K. Law. Ignition in the supersonic hydrogen\/air mixing layer with reduced mechanisms. J. Fluid Mech., 322:275\u2013296, 1996. DOI: https:\/\/doi.org\/10.1017\/S0022112096002790<\/a><\/li>\n\n\n\n
                                                2. B. T. Helenbrook, C. J. Sung, C. K. Law, and Wm. T. Ashurst. Stretchaffected flame propagation in vortical flows. Combustion and Flame, 104:460\u2013468, 1996.<\/li>\n<\/ol>\n\n\n\n

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