Dr Bishnu Lamichhane

Senior Lecturer

School of Mathematical and Physical Sciences (Mathematics)

Career Summary

Biography

Research Expertise
Numerical Methods for Partial Differential Equations, Mixed and Hybrid Finite Element Methods, Domain Decomposition Methods, Non-conforming Discretization Techniques, Nearly Incompressible Elasticity, Approximation Theory, Subset Selection & Variational Methods in Image Processing.

Qualifications

  • Doktor Der Naturwissenschaften (equiv PhD), Universitat Stuttgart
  • Master of Science, Universitat Kaiserslautern

Keywords

  • Approximation Theory
  • Differential Equations
  • Domain Decomposition
  • Finite Element Method
  • Mathematical Modelling
  • Mortar Finite Element
  • Numerical Analysis
  • Numerical Analysis
  • Numerical Method for Nearly Incompressible Elasticity
  • Vector Calculus

Languages

  • German (Fluent)
  • Hindi (Fluent)
  • Nepali (Fluent)

Fields of Research

Code Description Percentage
019999 Mathematical Sciences not elsewhere classified 100

Professional Experience

UON Appointment

Title Organisation / Department
Senior Lecturer University of Newcastle
School of Mathematical and Physical Sciences
Australia
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Publications

For publications that are currently unpublished or in-press, details are shown in italics.


Book (1 outputs)

Year Citation Altmetrics Link
2011 Lamichhane BP, Higher Order Mortar Finite Elements with Dual Lagrange Multipliers: Theory and Applications of Higher Order Mortar Finite Element Techniques, Lambert Academic Publishers, Saarbrucken, 200 (2011) [A2]

Chapter (2 outputs)

Year Citation Altmetrics Link
2012 Lamichhane BP, 'Two finite element methods for nearly incompressible linear elasticity using simplicial meshes', Advances in Mathematics Research, Nova Science, New York 157-187 (2012) [B1]
2009 Lamichhane BP, Rebollo-Neira L, 'Projection and interpolation based techniques for structured and impulsive noise filtering', New Signal Procesing Research, Nova Science Publisher, New York 127-158 (2009) [B1]

Journal article (35 outputs)

Year Citation Altmetrics Link
2015 Lamichhane BP, 'A new stabilization technique for the nonconforming Crouzeix-Raviart element applied to linear elasticity', APPLIED MATHEMATICS LETTERS, 39 35-41 (2015) [C1]
DOI 10.1016/j.aml.2014.08.005
2015 Lamichhane BP, 'A new stabilization technique for the nonconforming Crouzeix-Raviart element applied to linear elasticity', Applied Mathematics Letters, 39 35-41 (2015) [C1]
DOI 10.1016/j.aml.2014.08.005
2015 Lamichhane BP, Roberts SG, Stals L, 'A Mixed Finite Element Discretisation of Thin Plate Splines Based on Biorthogonal Systems', Journal of Scientific Computing, (2015)

The thin plate spline method is a widely used data fitting technique as it has the ability to smooth noisy data. Here we consider a mixed finite element discretisation of the thin... [more]

The thin plate spline method is a widely used data fitting technique as it has the ability to smooth noisy data. Here we consider a mixed finite element discretisation of the thin plate spline. By using mixed finite elements the formulation can be defined in-terms of relatively simple stencils, thus resulting in a system that is sparse and whose size only depends linearly on the number of finite element nodes. The mixed formulation is obtained by introducing the gradient of the corresponding function as an additional unknown. The novel approach taken in this paper is to work with a pair of bases for the gradient and the Lagrange multiplier forming a biorthogonal system thus ensuring that the scheme is numerically efficient, and the formulation is stable. Some numerical results are presented to demonstrate the performance of our approach. A preconditioned conjugate gradient method is an efficient solver for the arising linear system of equations.

DOI 10.1007/s10915-015-0068-6
2014 Lamichhane BP, 'A finite element method for a biharmonic equation based on gradient recovery operators', BIT NUMERICAL MATHEMATICS, 54 469-484 (2014) [C1]
DOI 10.1007/s10543-013-0462-0
2014 Droniou J, Lamichhane BP, 'Gradient schemes for linear and non-linear elasticity equations', Numerische Mathematik, (2014)

The gradient scheme framework provides a unified analysis setting for many different families of numerical methods for diffusion equations. We show in this paper that the gradient... [more]

The gradient scheme framework provides a unified analysis setting for many different families of numerical methods for diffusion equations. We show in this paper that the gradient scheme framework can be adapted to elasticity equations, and provides error estimates for linear elasticity and convergence results for non-linear elasticity. We also establish that several classical and modern numerical methods for elasticity are embedded in the gradient scheme framework, which allows us to obtain convergence results for these methods in cases where the solution does not satisfy the full (Formula presented.)-regularity or for non-linear models. © 2014 Springer-Verlag Berlin Heidelberg.

DOI 10.1007/s00211-014-0636-y
2014 Lamichhane BP, 'A stabilized mixed finite element method based on g-biorthogonal systems for nearly incompressible elasticity', COMPUTERS & STRUCTURES, 140 48-54 (2014) [C1]
DOI 10.1016/j.compstruc.2014.02.008
Citations Scopus - 1Web of Science - 1
2014 Lamichhane BP, 'A nonconforming finite element method for the Stokes equations using the Crouzeix-Raviart element for the velocity and the standard linear element for the pressure', INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 74 222-228 (2014) [C1]
DOI 10.1002/fld.3848
2014 Lamichhane BP, 'A mixed finite element method for nearly incompressible elasticity and Stokes equations using primal and dual meshes with quadrilateral and hexahedral grids', Journal of Computational and Applied Mathematics, 260 356-363 (2014) [C1]

We consider a mixed finite element method for approximating the solution of nearly incompressible elasticity and Stokes equations. The finite element method is based on quadrilate... [more]

We consider a mixed finite element method for approximating the solution of nearly incompressible elasticity and Stokes equations. The finite element method is based on quadrilateral and hexahedral triangulation using primal and dual meshes. We use the standard bilinear and trilinear finite element space enriched with element-wise defined bubble functions with respect to the primal mesh for the displacement or velocity, whereas the pressure space is discretized by using a piecewise constant finite element space with respect to the dual mesh. © 2013 Elsevier B.V. All rights reserved.

DOI 10.1016/j.cam.2013.09.056
Citations Web of Science - 1
2014 Lamichhane BP, Roberts SG, Hegland M, 'A new multivariate spline based on mixed partial derivatives and its finite element approximation', APPLIED MATHEMATICS LETTERS, 35 82-85 (2014) [C1]
DOI 10.1016/j.aml.2013.11.008
2013 Lamichhane BP, 'A New Finite Element Method for Darcy-Stokes-Brinkman Equations', ISRN Computational Mathematics, 2013 1-4 (2013) [C1]
2013 Lamichhane BP, McBride AT, Reddy BD, 'A finite element method for a three-field formulation of linear elasticity Cross Mark based on biorthogonal systems', COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 258 109-117 (2013) [C1]
DOI 10.1016/j.cma.2013.02.008
Citations Scopus - 2Web of Science - 2
2013 Lamichhane BP, 'Two simple finite element methods for Reissner-Mindlin plates with clamped boundary condition', Applied Numerical Mathematics, 72 91-98 (2013) [C1]

We present two simple finite element methods for the discretization of Reissner-Mindlin plate equations with clamped boundary condition. These finite element methods are based on ... [more]

We present two simple finite element methods for the discretization of Reissner-Mindlin plate equations with clamped boundary condition. These finite element methods are based on discrete Lagrange multiplier spaces from mortar finite element techniques. We prove optimal a priori error estimates for both methods. The first approach is based on a so-called standard Lagrange multiplier space for the mortar finite element method, where the Lagrange multiplier basis functions are continuous. The second approach is based on a so-called dual Lagrange multiplier space, where the Lagrange multiplier basis functions are discontinuous. The advantage of using the second approach is that easy static condensation of degrees of freedom corresponding to the Lagrange multiplier is possibly leading to a symmetric positive definite formulation. © 2013 IMACS. Published by Elsevier B.V. All rights reserved.

DOI 10.1016/j.apnum.2013.04.005
Citations Scopus - 1Web of Science - 1
2013 Lamichhane BP, McBride AT, Reddy BD, 'A finite element method for a three-field formulation of linear elasticity based on biorthogonal systems', Computer Methods in Applied Mechanics and Engineering, 258 109-117 (2013) [C1]

We consider a mixed finite element method based on simplicial triangulations for a three-field formulation of linear elasticity. The three-field formulation is based on three unkn... [more]

We consider a mixed finite element method based on simplicial triangulations for a three-field formulation of linear elasticity. The three-field formulation is based on three unknowns: displacement, stress and strain. In order to obtain an efficient discretization scheme, we use a pair of finite element bases forming a biorthogonal system for the strain and stress. The biorthogonality relation allows us to statically condense out the strain and stress from the saddle-point system leading to a symmetric and positive-definite system. The strain and stress can be recovered in a post-processing step simply by inverting a diagonal matrix. Moreover, we show a uniform convergence of the finite element approximation in the incompressible limit. Numerical experiments are presented to support the theoretical results. © 2013 Elsevier B.V.

DOI 10.1016/j.cma.2013.02.008
Citations Scopus - 2Web of Science - 2
2013 Lamichhane BP, Hegland M, 'A stabilised mixed finite element method for thin plate splines based on biorthogonal systems', Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal, 54 C72-C87 (2013) [C1]
2013 Lamichhane BP, 'Mixed Finite Element Methods for the Poisson Equation Using Biorthogonal and Quasi-Biorthogonal Systems', Advances in Numerical Analysis, 2013 1-9 (2013) [C1]
DOI 10.1155/2013/189045
2011 Lamichhane BP, 'A stabilized mixed finite element method for the biharmonic equation based on biorthogonal systems', Journal of Computational and Applied Mathematics, 235 5188-5197 (2011) [C1]
DOI 10.1016/j.cam.2011.05.005
Citations Scopus - 3Web of Science - 2
2011 Lamichhane BP, Stephan EP, 'A symmetric mixed finite element method for nearly incompressible elasticity based on biorthogonal systems', Numerical Methods for Partial Differential Equations, 28 1336-1353 (2011) [C1]
DOI 10.1002/num.20683
Citations Scopus - 3Web of Science - 4
2011 Lamichhane BP, 'A mixed finite element method for the biharmonic problem using biorthogonal or quasi-biorthogonal systems', Journal of Scientific Computing, 46 379-396 (2011) [C1]
DOI 10.1007/s10915-010-9409-7
Citations Scopus - 3Web of Science - 3
2010 Lamichhane BP, 'A gradient recovery operator based on an oblique projection', Electronic Transactions on Numerical Analysis, 37 166-172 (2010) [C1]
Citations Scopus - 1Web of Science - 1
2009 Lamichhane BP, 'Mortar finite elements for coupling compressible and nearly incompressible materials in elasticity', INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 6 177-192 (2009) [C1]
Citations Scopus - 3Web of Science - 2
2009 Falletta S, Lamichhane BP, 'Mortar finite elements for a heat transfer problem on sliding meshes', CALCOLO, 46 131-148 (2009) [C1]
DOI 10.1007/s10092-009-0001-1
Citations Scopus - 1Web of Science - 1
2009 Lamichhane BP, 'A mixed finite element method for non-linear and nearly incompressible elasticity based on biorthogonal systems', INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 79 870-886 (2009) [C1]
DOI 10.1002/nme.2594
Citations Scopus - 6Web of Science - 7
2009 Lamichhane BP, 'From the Hu-Washizu formulation to the average nodal strain formulation', COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 198 3957-3961 (2009) [C1]
DOI 10.1016/j.cma.2009.09.008
Citations Scopus - 10Web of Science - 11
2009 Lamichhane BP, 'Inf-sup stable finite-element pairs based on dual meshes and bases for nearly incompressible elasticity', IMA JOURNAL OF NUMERICAL ANALYSIS, 29 404-420 (2009) [C1]
DOI 10.1093/imanum/drn013
Citations Scopus - 15Web of Science - 14
2009 Lamichhane BP, 'Finite Element Techniques for Removing the Mixture of Gaussian and Impulsive Noise', IEEE TRANSACTIONS ON SIGNAL PROCESSING, 57 2538-2547 (2009) [C2]
DOI 10.1109/TSP.2009.2016272
Citations Scopus - 5Web of Science - 2
2008 Lamichhane BP, 'A mixed finite element method based on a biorthogonal system for nearly incompressible elastic problems', ANZIAM Journal, 50 324-338 (2008) [C1]
DOI 10.0000/anziamj.v50i0.1422
Citations Scopus - 2
2007 Chavan KS, Lamichhane BP, Wohlmuth BI, 'Locking-free finite element methods for linear and nonlinear elasticity in 2D and 3D', Computer Methods in Applied Mechanics and Engineering, 196 4075-4086 (2007)

The uniform convergence of finite element approximations based on a modified Hu-Washizu formulation for the nearly incompressible linear elasticity is analyzed. We show the optima... [more]

The uniform convergence of finite element approximations based on a modified Hu-Washizu formulation for the nearly incompressible linear elasticity is analyzed. We show the optimal and robust convergence of the displacement-based discrete formulation in the nearly incompressible case with the choice of approximations based on quadrilateral and hexahedral elements. These choices include bases that are well known, as well as newly constructed bases. Starting from a suitable three-field problem, we extend our a-dependent three-field formulation to geometrically nonlinear elasticity with Saint-Venant Kirchhoff law. Additionally, an a-dependent three-field formulation for a general hyperelastic material model is proposed. A range of numerical examples using different material laws for small and large strain elasticity is presented. © 2007 Elsevier B.V. All rights reserved.

DOI 10.1016/j.cma.2007.03.022
Citations Scopus - 12
2006 Lamichhane BP, Wohlmuth BI, 'Biorthogonal bases with local support and approximation properties', MATHEMATICS OF COMPUTATION, 76 233-249 (2006)
Citations Scopus - 10
2006 Lamichhane BP, Reddy BD, Wohlmuth BI, 'Convergence in the incompressible limit of finite element approximations based on the Hu-Washizu formulation', NUMERISCHE MATHEMATIK, 104 151-175 (2006)
DOI 10.1007/s00211-006-0014-5
Citations Scopus - 15Web of Science - 16
2006 Djoko JK, Lamichhane BP, Reddy BD, Wohmuth BI, 'Conditions for equivalence between the Hu-Washizu and related formulations, and computational behavior in the incompressible limit', COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 195 4161-4178 (2006)
DOI 10.1016/j.cma.2005.07.018
Citations Scopus - 20Web of Science - 19
2005 Lamichhane BP, Wohlmuth BI, 'Mortar finite elements with dual Lagrange multipliers: Some applications', DOMAIN DECOMPOSITION METHODS IN SCIENCE AND ENGINEERING, 40 319-326 (2005)
2005 Lamichhane BP, Stevenson RP, Wohlmuth BI, 'Higher order mortar finite element methods in 3D with dual lagrange multiplier bases', NUMERISCHE MATHEMATIK, 102 93-121 (2005)
DOI 10.1007/s00211-005-0636-z
Citations Scopus - 19Web of Science - 13
2004 Lamichhane BP, Wohlmuth BI, 'Mortar finite elements for interface problems', COMPUTING, 72 333-348 (2004)
DOI 10.1007/s00607-003-0062-y
Citations Scopus - 19Web of Science - 20
2004 Lamichhane BP, Wohlmuth BI, 'A quasi-dual Lagrange multiplier space for serendipity mortar finite elements in 3D', ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 38 73-92 (2004)
DOI 10.1051/m2an:2004004
Citations Scopus - 3Web of Science - 2
2002 Lamichhane BP, Wohlmuth BI, 'Higher order dual Lagrange multiplier spaces for mortar finite element discretizations', CALCOLO, 39 219-237 (2002)
DOI 10.1007/s100920200010
Citations Scopus - 10Web of Science - 9
Show 32 more journal articles

Conference (4 outputs)

Year Citation Altmetrics Link
2013 Lamichhane BP, 'A mixed finite element method for the biharmonic problem using biorthogonal or quasi-biorthogonal systems', Proceedings of the 49th ANZIAM Conference, Newcastle, NSW (2013) [E3]
2012 Lamichhane BP, Hegland M, 'A stabilised mixed finite element method for thin plate splines based on biorthogonal systems', Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal, Brisbane (2012) [C1]
2011 Andersson RS, Lamichhane BP, 'Piecewise constant aquifer parameter identification recovery', MODSIM 2011: 19th International Congress on Modelling and Simulation Proceedings, Perth (2011) [E1]
2011 Lamichhane BP, Roberts S, Stals L, 'A mixed finite element discretisation of thin-plate splines', Proceedings of the Fifteenth Biennial Conference on Computational Techniques and Applications Conference (CTAC10), Sydney, Australia (2011) [E1]
Show 1 more conference
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Grants and Funding

Summary

Number of grants 2
Total funding $25,000

Click on a grant title below to expand the full details for that specific grant.


20141 grants / $20,000

Efficient approximation techniques for partial differential equations of solid and fluid mechanics$20,000

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Doctor Bishnu Lamichhane
Scheme Near Miss Grant
Role Lead
Funding Start 2014
Funding Finish 2014
GNo G1301386
Type Of Funding Internal
Category INTE
UON Y

20111 grants / $5,000

Finite Element Methods for Solving Partial Differential Equations$5,000

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Doctor Bishnu Lamichhane
Scheme New Staff Grant
Role Lead
Funding Start 2011
Funding Finish 2011
GNo G1100303
Type Of Funding Internal
Category INTE
UON Y
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Research Supervision

Number of supervisions

Completed0
Current2

Total current UON EFTSL

PhD1

Current Supervision

Commenced Level of Study Research Title / Program / Supervisor Type
2015 PhD Mixed Finite Element Method for Wave Type Equations
Mathematics, Faculty of Science and Information Technology, The University of Newcastle
Principal Supervisor
2012 PhD Reflection and Projection Methods for non-convex inverse problems
Mathematics, Faculty of Science and Information Technology, The University of Newcastle
Co-Supervisor
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Dr Bishnu Lamichhane

Position

Senior Lecturer
School of Mathematical and Physical Sciences
Faculty of Science and Information Technology

Focus area

Mathematics

Contact Details

Email bishnu.lamichhane@newcastle.edu.au
Phone (61-2) 49215529
Mobile 0422437170
Fax (61-2) 4921 6898

Office

Room V127
Building Mathematics Building - V127
Location Callaghan NSW 2308 Australia
University Drive
Callaghan, NSW 2308
Australia
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