Publikationen

Monographien

• Kollokationsverfahren und Mehrgittermethoden bei elliptischen Randwertaufgaben. GMD-Bericht Nr. 168, Oldenbourg-Verlag, Oldenbourg 1987
• Efficient iterative solution of spectral systems for the Navier-Stokes equations. Verlag Dr. Köster, Berlin 1994 

Veröffentlichungen in Fachzeitschriften

• Line relaxation for spectral multigrid methods. J. Comput. Phys. 77, 166-182 (1988)
• Multigrid methods for combined finite difference and Fourier problems. J. Comput. Phys. 78, 424-436 (1988)
• Collocation and full multigrid methods. Appl. Math. Comput. 28, 35-45 (1988)
• Konvergenzaussagen für Kollokationsverfahren bei elliptischen Randwertaufgaben. Numer. Math. 54, 619-637 (1989)
• Spectral methods with sparse matrices. Numer. Math. 56, 25-41 (1989)
• Improved condition number for spectral methods. Math. of Comp. 53, 103-119 (1989)
• A 3D spectral multigrid method. Appl. Math. Comp. 41, 117-128 (1991)
• Some results about the pseudospectral approximation of one-dimensional fourth-order problems. Numer. Math. 58, 399-419 (1990) (gemeinsam mit D. Funaro)
• Algebraic spectral multigrid methods. Comput. Meth. Appl. Mech. 80, 281-289 (1990)
• Einschliessungsaussagen bei Systemen semilinearer parabolischer Differentialgleichungen. Appl. of Math. 36,96-122 (1991)
• Spectral collocation methods and polar coordinate singularities, J. Comput. Phys. 96, 241-257 (1991) (gemeinsam mit H. Eisen und K. Witsch)
• A stabilized treatment of the biharmonic operator with spectral methods. SIAM J. Scient. and Stat. Comput. 12, 1162-1172 (1991)
• A new method of stabilization for singular perturbation problems with spectral methods. SIAM J. Numer. Anal. 29, 107-122 (1992) (gemeinsam mit H.Eisen)
• Stabilization techniques for spectral methods, J. Scient. Comput. 6, No. 1, 1-19 (1991)
• A stabilized multidomain approach for singular perturbation problems. J. Scient. Comput. 7, No. 2, 95-125 (1992)
• Spectral multigrid techniques for the Stokes problem in streamfunction formulation, J. Comput. Phys. 102, 310-318 (1992)
• Strong convergence estimates for pseudospectral methods, Appl. Math. 37, No. 6, 401-417 (1992)
• Splitting techniques for the pseudospectral approximation of the unsteady Stokes equations, SIAM J. Numer. Anal. 30, No. 1, 19-40 (1993)
• Domain decomposition for fourth order problems, SIAM J. Numer. Anal. 30, No. 2, 435-453 (1993)
• Spectral projective Newton methods for quasilinear elliptic boundary value problems, Calcolo 29, Nos. 1-2, 33-48 (1993)
• Spectral multigrid techniques for the Navier-Stokes equations, Comput. Meth. Appl. Mech. Eng. 106, 297-314 (1993)
• Spectral multigrid methods for the reformulated Stokes equations, J. Comp. Phys. 107, 213-224 (1993)
• Finite element preconditioning for spectral multigrid methods, Appl. Math. Comput. 59, No. 1, 19-40 (1993)
• Spectral multigrid methods for domain decomposition problems using patching techniques, Appl. Math. Comput. 59, No. 2, 165-176 (1993)
• Distributive relaxations for the spectral Stokes operator, J. Scient. Comput. 8, No. 4, 389-398 (1993)
• Spectral viscosity for convection dominated flow, J. Scient. Comput. 9, No. 2, 137-147 (1994)
• Spectral methods for singular perturbation problems, Appl. Math. 39, No. 3, 161-188 (1994)
• Defect correction for the advection-diffusion equation, Comput. Meth. Appl. Mech. Eng. 119,191-197 (1994)
• Defect correction for convection dominated flow , SIAM J. Scient. Comput. 17, 1082-1091 (1996)
• High order time splitting techniques for the Stokes equations, J. Scient. Comput. 11, No. 4, 397-410 (1996)
• Pseudospectral Approximation of the unsteady Stokes Equations SIAM J. Numer. Anal. 35, 1646-1662 (1998) 
• Spectral collocation on triangular elements J. Comput. Phys. 145, No. 2, 743-757 (1998)
• Spectral approximation of third-order problems , J. Scient. Comput. 14, No. 3, 275-289 (1999)
• Splitting techniques for the Navier-Stokes equations, eingereicht bei SIAM J. Numer. Anal., 1998
• Spektrale Mehrgittermethoden für die volle Potentialgleichung, eingereicht bei Computing (gemeinsam mit R. Starke und K. Witsch)
• Parallelism in finite element and spectral codes, in Vorbereitung.
• Splitting techniques with staggered grids for the Navier-Stokes equations , J. Comput. Phys. 168, No. 1, 131-154 (2001) (gemeinsam mit H. Haschke)
• Spectral schemes on triangular elements , J. Comput. Phys. 173, No. 1, 279-301 (2001) (gemeinsam mit B. Loch)
• Least-Squares Spectral Collocation for Discontinuous and Singular Pertubation Problems , J. of Comp. and Appl. Math., 157, No. 2, 329-345 (2003)
• Spectral collocation schemes on the unit disc , J. of Comp. Phys. 199, 66-86 (2004) 
• Least-Squares Spectral Collocation for the Navier--Stokes Equations
  (ps)  J. Scient. Comput. 21, No. 1, 81-90(2004)
• Improved Lebesgue constants on the triangle , J. of Comp. Phys. 207, 625-638 (2005)
•  Least-Squares Spectral Collocation with the Overlapping Schwarz Method for the Incompressible Navier-Stokes Equations , Numer. Alg. 43, 61-73 (2006)
• An adaptive least-squares spectral collocation method with triangular elements for the incompressible Navier-Stokes equations (ps-file as zip), J. Eng. Math. 56, 337-350 (2006)
• An adaptive spectral least-squares scheme for the Burgers equation, Numer. Alg. 1, 1-10 (2007)
• A direct solver for the least-squares spectral collocation system on rectangular elements for the incompressible Navier-Stokes equations (pdf), J. Comput. Phys. 227, No. 9, 4776-4796 (2008), (gemeinsam mit Th. Kattelans)
• A splitting technique of higher order for the Navier-Stokes equations (pdf), J. Comput. Appl. Math. 228, No. 1, 373-390 (2009), (gemeinsam mit J. Frochte)
• Conservation of mass and momentum of the least-squares spectral collocation scheme for the Stokes problem (pdf), J. Comput. Phys. 228, No. 13, 4649-4664 (2009), (gemeinsam mit Th. Kattelans)
• Mass and momentum conservation of the least-squares spectral collocation method for the Navier-Stokes equations (pdf), J. of Comp. and Appl. Math. 236, No. 6, 1193-1215 (2011), (gemeinsam mit Th. Kattelans)

Veröffentlichungen in Tagungsberichten

• Effective preconditioning for spectral multigrid methods, in Robust Multi-Grid Methods (Wolfgang Hackbusch, Ed.), Notes on Numerical Fluid Mechanics (Vol. 23), Vieweg-Verlag, Braunschweig-Wiesbaden 1988
• Spectral discretization giving a sparse matrix. ZAMM 69, 195-197 (1989)
• Algebraic spectral multigrid methods, in Spectral and High Order Methods for Partial Differential Equations. Proceedings of the ICOSAHOM'89 Conference (C.Canuto and A.Quarteroni, eds.), Como, Elsevier Science Publishers B.V., North Holland, 281-289 (1990)
• Domain decomposition for the approximation of fourth order problems. ZAMM 71, T574-T576 (1991)
• Spectral multigrid techniques for the Stokes problem in streamfunction formulation, in Multigrid Methods: Special Topics and Applications II, GMD-Studien Nr. 189, GMD St. Augustin, 139-154 (1991)
• Finite element versus finite difference preconditioning for spectral multigrid methods, in Proceedings of the IMACS International Symposium on Iterative Methods in Linear Algebra, Brüussel, 203-209 (1992)
• Domain decomposition for the Stokes equations in streamfunction formulation, in Proceedings of the Sixth Int. Conf. on Domain Decomposition Methods in Science and Engineering, Como, 263-271 (1992)
• Spectral multigrid methods for the reformulated Navier-Stokes equations, erscheint in Spectral and High Order Methods for Partial Differential Equations. Proceedings of the ICOSAHOM'92 Conference (C.Bernardi and Y.Maday, eds.), Montpellier, 1992
• Splitting techniques for the pseudospectral approximation of the unsteady Stokes equations, ZAMM 73, T717-T719 (1993)
• Spectral multigrid methods for the reformulated Stokes equations, CWI Tract, Contributions to multigrid, A selection of contributions to the 4th Multigrid Conference, Amsterdam, P.W. Hemker, P. Wesseling (eds.), July 6-9, 67-75 (1993)
• Defect correction for convection dominated flow,  in Proceedings of the International Workshop on Numerical Methods for the Navier-Stokes Equations, Notes on Numerical Fluid Mechanics 47, F.-K. Hebeker, R. Rannacher and G. Wittum (eds.), Heidelberg, 111-121 (1993)
• Spectral multigrid for the reformulated Navier-Stokes equations, ZAMM  74, T579-T580 (1994)
• Defect correction for convection-diffusion problems, ZAMM, 1995
• Defect correction for convection dominated flow,  in Spectral and High Order Methods for Partial Differential Equations. Proceedings of the ICOSAHOM'95 Conference (R. Scott, ed.), Houston Journal of Mathematics, 559-567, Houston, 1996
• Operator splitting for the unsteady Stokes equations,  in Conference on Parallel Computational Fluid Dynamics (P.Schiano, CIRA), Capri, May 20-23, 1996, 344-352, Elsevier Science B.V., Amsterdam 1997
• Defect correction for convection dominated flow,  in Proceedings of The Ninth International Conference on Domain Decomposition (P.E.Bjorstad), Bergen, Norway, June 1996
• Operator splitting for the unsteady Stokes equations,  in Proceedings of the Fifth European Multigrid Conference (G. Wittum, ed.), 101-113, Stuttgart, 1998 
• High order splitting techniques for the Navier-Stokes equations, ZAMM 1997
• Operator splitting for the Navier-Stokes equations,  in Proceedings of the ENUMATH'97 (R. Rannacher, ed.), Heidelberg, October 1997 
• Operator Splitting for the Stokes Equations , in Proceedings of the Fifth European Multigrid Conference, ed. G. Wittum, 101-113, Stuttgart 1998
• An adaptive operator splitting of higher order for the Navier-Stokes equations, in Proceedings of the ENUMATH 2005 (A.Bermudez,D.Gomez,P.Quintel,P.Salgado, ed.), Santiago de Compostela, 871-879, Springer 2006. joint work with Jörg Frochte (pdf)
• A least-squares spectral collocation scheme with improved stability for the Stokes and the Navier-Stokes equations (pdf), in Proceedings of the ICNAAM 2008 (T.E. Simos, G. Psihoyios, Ch. Tsitouras, ed.), Psalidi (Kos, Greece), AIP Conference Proceedings 1048, 307-310 (2008) (joint work with Th. Kattelans)
• Mass and momentum conservation of the Least-Squares Spectral Collocation Method for the time-dependent Stokes equations (pdf), Proceedings of the ICNAAM 2009 (T.E. Simos, G. Psihoyios, Ch. Tsitouras, ed.), Rethymno (Crete, Greece), AIP Conference Proceedings 1168, 197-201 (2009) (joint work with Th. Kattelans) 
   

Download

• Defect Correction for convection-dominated Flow 
  veröffentlicht in SIAM J. Sci. Comput. 17, 1082-1091 (1996) 
   
• Defect Correction for the Advection-Diffusion Equation 
  veröffentlicht in Comput. Meth. Appl. Mech. Eng. 119, 191-197 (1994)
   
• Operator Splitting for the Stokes Equations 
  veröffentlicht in Proceedings of the Fifth European Multigrid Conference, ed. G. Wittum, 101-113, Stuttgart 1998 
   
• Pseudospectral Approximation of the unsteady Stokes Equations veröffentlicht in SIAM J. Numer. Anal. 35 (4), 1646-1662 (1998) 
   
• Spectral Collocation on Triangular Elements 
  veröffentlicht in J. Comput. Phys. 145, 743-757 (1998) 
   
• Spectral Approximation of Third-Order Problems 
  veröffentlicht in J. of Scientific Computing 14, No. 3, 275-289 (1999) 
   
• Splitting Techniques with Staggered Grids for the Navier-Stokes Equations 
  von H. Haschke und W. Heinrichs, veröffentlicht in Journ. Comput. Phys. 168, No. 1, 131-154 (2001)
   
• Spectral Schemes on Triangular Elements
  von W. Heinrichs und B. Loch, J. Comput. Phys. 173, No. 1, 279-301(2001) 
   
• First-Order System Least-Squares for the Spectral Approximation of Second-Order Elliptic Problems
  von W.Heinrichs 
   
• Nonconforming Spectral Collocation 
  von W.Heinrichs 
   
• An Interface Relaxation for the Patching of Spectral Collocation and Finite Difference Schemes
  von W.Heinrichs 
   
• Least-Squares Spectral Collocation for the Stokes Problem
  von W.Heinrichs 
   
• Spectral Collocation on the Unit Disc without Polar Coordinates (ps) (pdf) 
  von W.Heinrichs 
   
• Improved Condition Number for Spectral Collocation on the Unit Disc (ps) (pdf) 
  von W.Heinrichs 
   
• Splitting Techniques with Finite Differences on nonstaggered grids for the Navier-Stokes-Equation (ps) von W.Heinrichs
   
• Convergence of Chebyshev Spectral Approximations for Eigenvalues and Eigenfunctions of discontinuous problems (ps) von W.Heinrichs 
   
• An adaptive spectral least-squares scheme for the Burgers equation, veröffentlicht in Numer. Alg. 1, 1-10 (2007) 
   
• An adaptive least-squares spectral collocation method with triangular elements for the incompressible Navier-Stokes equations (ps als zip-File), veröffentlicht in J. Eng. Math. 56, 337-350 (2006) 
   
• Least-Squares Spectral Collocation with the Overlapping Schwarz Method for the Incompressible Navier-Stokes Equations 
  veröffentlicht in Numer. Alg. 43, 61-73 (2006)  
   
•  A direct solver for the least-squares spectral collocation system on rectangular elements for the Stokes equations 
  von W. Heinrichs und Th. Kattelans
   
• A splitting technique of higher order for the Navier-Stokes equations 
  von J. Frochte und W. Heinrichs, veröffentlicht in J. Comput. Appl. Math. 228, No. 1, 373-390 (2009)  
   
• A direct solver for the least-squares spectral collocation system on rectangular elements for the incompressible Navier-Stokes equations 
  von W. Heinrichs und Th. Kattelans, veröffentlicht in J. Comput. Phys. 227, No. 9, 4776-4796 (2008)
   
• A least-squares spectral collocation scheme with improved stability for the Stokes and the Navier-Stokes equations 
  von W. Heinrichs und Th. Kattelans, veröffentlicht in AIP Conference Proceedings 1048, 307-310 (2008) 
   
• Conservation of mass and momentum of the least-squares spectral collocation scheme for the Stokes problem 
  von W. Heinrichs und Th. Kattelans , veröffenticht im J. Comput. Phys. 228, No. 13, 4649-4664 (2009) 
   
• Spektrale Least-Squares Verfahren für die Konvektions-Diffusions-Gleichung 
  Diplomarbeit von J. Kippar (2009) 


• Mass and momentum conservation of the Least-Squares Spectral Collocation Method for the time-dependent Stokes equations 
  von W. Heinrichs und Th. Kattelans, accepted 


• Mass and momentum conservation of the Least-Squares Spectral Collocation Method for the Navier-Stokes equations 
  von W. Heinrichs und Th. Kattelans 


• The Least-Squares Spectral Collocation Method for the Stokes and the Navier-Stokes equations: Conservation of mass and momentum 
  von W. Heinrichs und Th. Kattelans 


• Adaptive spektrale Least-Squares Verfahren für Konvektions-Diffusions-Gleichung mit Triangulierung 
  Diplomarbeit von F. Mehdizadeh-Latreh (2013) 


• Dreiecksbasierte spektrale Mehrgitterverfahren für elliptische Probleme 
  Diplomarbeit von P. Norek (2014) 
• Eine spektrale Least-Squares Kollokationsmethode auf Dreieckselementen und ihre Anwendung zur Lösung elliptischer und Navier-Stokes-Gleichungen Dissertation von R. Rajadiram (2019)
• Adaptive spectral least-squares techniques for reaction-diffusion equations Dissertation von P. Marquardt (2020)
• Adaptive least squares pseudospectral element methods for the two dimensional Euler equations Dissertation vom I. Pinger (2020)
• Numerische Stabilitätsanalyse von Spektralmethoden für zeitabhängige partielle Differentialgleichungen Masterarbeit von S. Leitgeber (2021)