Wissenschaftliche Artikel

Faustmann, M., Marcati, C., Melenk, J. M., & Schwab, C. (2023). Exponential Convergence of hp-FEM for the Integral Fractional Laplacian in Polygons. SIAM Journal on Numerical Analysis, 61(6), 2601–2622. https://doi.org/10.1137/22M152493X ( reposiTUm)
Angleitner, N., Faustmann, M., & Melenk, J. M. (2023). H-inverses for RBF interpolation. Advances in Computational Mathematics, 49(6), Article 85. https://doi.org/10.1007/s10444-023-10069-5 ( reposiTUm)
Faustmann, M., Stephan, E. P., & Wörgötter, D. (2023). Two-level error estimation for the integral fractional Laplacian. Computational Methods in Applied Mathematics, 23(3), 603–621. https://doi.org/10.1515/cmam-2022-0195 ( reposiTUm)
Angleitner, N., Faustmann, M., & Melenk, J. M. (2023). Exponential meshes and H-matrices. Computers and Mathematics with Applications, 130, 21–40. https://doi.org/10.1016/j.camwa.2022.11.011 ( reposiTUm)
Faustmann, M., Melenk, J. M., & Parvizi, M. (2022). 𝘏-matrix approximability of inverses of FEM matrices for the time-harmonic Maxwell equations. Advances in Computational Mathematics, 48(5), Article 59. https://doi.org/10.1007/s10444-022-09965-z ( reposiTUm)
Faustmann, M., Marcati, C., Melenk, J. M., & Schwab, C. (2022). Weighted Analytic Regularity for the Integral Fractional Laplacian in Polygons. SIAM Journal on Mathematical Analysis, 54(6), 6323–6357. https://doi.org/10.1137/21M146569X ( reposiTUm)
Faustmann, M., Karkulik, M., & Melenk, J. M. (2022). Local Convergence of the FEM for the Integral Fractional Laplacian. SIAM Journal on Numerical Analysis, 60(3), 1055–1082. https://doi.org/10.1137/20M1343853 ( reposiTUm)
Faustmann, M., Melenk, J. M., & Parvizi, M. (2022). Caccioppoli-type estimates and H-matrix approximations to inverses for FEM-BEM couplings. Numerische Mathematik, 150, 849–892. https://doi.org/10.1007/s00211-021-01261-0 ( reposiTUm)
Faustmann, M., Melenk, J. M., & Praetorius, D. (2021). Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian. Mathematics of Computation, 90(330), 1557–1587. https://doi.org/10.1090/mcom/3603 ( reposiTUm)
Faustmann, M., Melenk, J. M., & Parvizi, M. (2021). On the stability of Scott-Zhang type operators and application to multilevel preconditioning in fractional diffusion. ESAIM: Mathematical Modelling and Numerical Analysis, 55(2), 595–625. https://doi.org/10.1051/m2an/2020079 ( reposiTUm)
Angleitner, N., Faustmann, M., & Melenk, J. M. (2021). Approximating inverse FEM matrices on non-uniform meshes with H-matrices. Calcolo, 58(31). https://doi.org/10.1007/s10092-021-00413-w ( reposiTUm)
Faustmann, M., & Melenk, J. M. (2018). Local convergence of the boundary element method on polyhedral domains. Numerische Mathematik, 140, 593–637. https://doi.org/10.1007/s00211-018-0975-1 ( reposiTUm)
Faustmann, M., Melenk, J. M., & Praetorius, D. (2017). Existence of H-matrix approximants to the inverse of BEM matrices: the hyper-singular integral operator. IMA Journal of Numerical Analysis, drw024. https://doi.org/10.1093/imanum/drw024 ( reposiTUm)
Faustmann, M., & Melenk, J. M. (2017). Robust exponential convergence of 𝒉𝒑-FEM in balanced norms for singularly perturbed reaction-diffusion problems: corner domains. Computers and Mathematics with Applications, 74(7), 1576–1589. https://doi.org/10.1016/j.camwa.2017.03.015 ( reposiTUm)
Faustmann, M., Melenk, J. M., & Praetorius, D. (2016). Existence of H-matrix approximants to the inverses of BEM matrices: the simple-layer operator. Mathematics of Computation, 85(297), 119–152. https://doi.org/10.1090/mcom/2990 ( reposiTUm)
Faustmann, M., Melenk, J. M., & Praetorius, D. (2015). H-matrix approximability of the inverses of FEM matrices. Numerische Mathematik, 131(4), 615–642. https://doi.org/10.1007/s00211-015-0706-9 ( reposiTUm)
Melenk, J. M., Faustmann, M., & Praetorius, D. (2012). Efficient and Robust Approximation of the Helmholtz Equation. Oberwolfach Reports, 9(4), 3305–3338. https://doi.org/10.4171/owr/2012/55 ( reposiTUm)

Beiträge in Tagungsbänden

Bahr, B., Faustmann, M., Marcati, C., Melenk, J. M., & Schwab, C. (2023). Exponential Convergence of hp-FEM for the Integral Fractional Laplacian in 1D. In J. M. Melenk, I. Perugia, J. Schöberl, & C. Schwab (Eds.), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 : Selected Papers from the ICOSAHOM Conference, Vienna, Austria, July 12-16, 2021 (pp. 291–306). Springer. https://doi.org/10.1007/978-3-031-20432-6_18 ( reposiTUm)
Faustmann, M., Marcati, C., Melenk, J. M., & Schwab, C. (2023). Exponential convergence of hp-FEM for the integral fractional Laplacian. In Book of Abstract: 9th International Conference on High Order Finite Element and Isogeometric Methods (pp. 47–47). ( reposiTUm)
Faustmann, M., Melenk, J. M., & Praetorius, D. (2014). A new proof for existence of H-matrix approximants to the inverse of FEM matrices: the Dirichlet problem for the Laplacian. In Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012 (pp. 249–259). Springer. https://doi.org/10.1007/978-3-319-01601-6_20 ( reposiTUm)

Präsentationen

Melenk, J. M., Bahr, B., Faustmann, M., Marcati, C., & Schwab, C. (2024, January 10). hp-FEM for the integral fractional Laplacian in polygons [Conference Presentation]. Conference on Advanced Numerical Methods for Non-local Problems 2024, Istanbul, Turkey. ( reposiTUm)
Faustmann, M., & Rieder, A. (2023, March 8). FEM-BEM Coupling in Fractional Diffusion [Conference Presentation]. Nonlocal Equations: Analysis and Numerics, Germany. ( reposiTUm)
Faustmann, M., Marcati, C., Melenk, J. M., & Schwab, C. (2023, June 29). Exponential convergence of hp-FEM for the integral fractional Laplacian [Conference Presentation]. 29th Biennial Conference on Numerical Analysis, Glasgow, United Kingdom of Great Britain and Northern Ireland (the). http://hdl.handle.net/20.500.12708/187176 ( reposiTUm)
Melenk, J. M., Bahr, B., Faustmann, M., Parvizi, M., & Praetorius, D. (2023, June 12). AFEM for the fractional Laplacian [Conference Presentation]. Foundations of Computational Mathematics (FoCM 2023), Paris, France. ( reposiTUm)
Faustmann, M., Marcati, C., Melenk, J. M., & Schwab, C. (2022). Analytic Regularity and hp-FEM for the Integral Fractional Laplacian. 19th European Finite Element Fair, Espoo, Finland, EU. http://hdl.handle.net/20.500.12708/123532 ( reposiTUm)
Bahr, B. H., Faustmann, M., Melenk, J. M., & Praetorius, D. (2022). Adaptive FEM for fractional diffusion. ESI Workshop “Adaptivity, High Dimensionality and Randomness,” Wien, Austria. http://hdl.handle.net/20.500.12708/123531 ( reposiTUm)
Melenk, J. M., Faustmann, M., Schwab, Ch., & Marcati, C. (2022, November). weighted analytic regularity for the integral fractional Laplacian [Presentation]. one world numerical analysis seminar, Germany. ( reposiTUm)
Melenk, J. M., Faustmann, M., Schwab, Ch., & Marcati, C. (2022, February). weighted analytic regularity for the integral fractional Laplacian [Keynote Presentation]. BI-discrete 2022, Bielefeld, Germany. ( reposiTUm)
Faustmann, M., Marcati, C., Melenk, J. M., & Schwab, Ch. (2022, August 31). Weighted analytic regularity for the integral fractional Laplacian in polygons [Conference Presentation]. Computational Methods in Applied Mathematics 2022, Wien, Austria. ( reposiTUm)
Melenk, J. M., Faustmann, M., Schwab, Ch., & Marcati, C. (2022, February). weighted analytic regularity for the integral fractional Laplacian [Keynote Presentation]. nonlocal operators at NUS, Singapore, Singapore. ( reposiTUm)
Faustmann, M., Marcati, C., Melenk, J. M., & Schwab, Ch. (2022, September 15). Weighted analytic regularity and hp-FEM for the integral fractional Laplacian [Conference Presentation]. Chemnitz FE Symposium 2022, Herrsching, Germany. ( reposiTUm)
Melenk, J. M., Faustmann, M., Schwab, Ch., & Marcati, C. (2022, November). weighted analytic regularity for the integral fractional Laplacian [Keynote Presentation]. Journees singulieres, France. ( reposiTUm)
Melenk, J. M., Faustmann, M., Schwab, Ch., & Marcati, C. (2022, November). weighted analytic regularity for the integral fractional Laplacian [Keynote Presentation]. BAIL 2022, Argentina. ( reposiTUm)
Melenk, J. M., Faustmann, M., & Karkulik, M. (2022, September). local error analysis for nonlocal operators [Conference Presentation]. Chemnitz FEM Symposium 2022 (Herrsching), Germany. http://hdl.handle.net/20.500.12708/154013 ( reposiTUm)
Melenk, J. M., Faustmann, M., & Karkulik, M. (2022, August). local error analysis for nonlocal operators [Keynote Presentation]. Boundary Elements and Friends, Innsbruck, Austria. http://hdl.handle.net/20.500.12708/154011 ( reposiTUm)
Faustmann, M., Karkulik, M., Melenk, J. M., & Praetorius, D. (2021). Finite Element Method for Fractional Diffusion - Recent Results. DMV-ÖMG Jahrestagung 2021, virtuelle Tagung - Zoom / Passau, EU. http://hdl.handle.net/20.500.12708/123387 ( reposiTUm)
Faustmann, M., Melenk, J. M., & Karkulik, M. (2020). Local convergence of the FEM for the integral fractional Laplacian. 4th Conference on Numerical Methods for Fractional-Derivative Problems, Peking (online), Non-EU. http://hdl.handle.net/20.500.12708/123101 ( reposiTUm)
Faustmann, M., Karkulik, M., Melenk, J. M., Parvizi, M., & Praetorius, D. (2020). The Fractional Laplacian - Adaptive FEM, Preconditioning and Local Errors. USM Seminar, Valparaiso (online), Non-EU. http://hdl.handle.net/20.500.12708/123102 ( reposiTUm)
Faustmann, M., Melenk, J. M., Parvizi, M., & Praetorius, D. (2019). Optimal adaptivity and preconditioning for the fractional Laplacian. 15th Austrian Numerical Analysis Day, Graz, Austria. http://hdl.handle.net/20.500.12708/122740 ( reposiTUm)
Faustmann, M. (2019). Wie das Dezimalsystem nach Europa kam. TUforMath, Wien, Austria. http://hdl.handle.net/20.500.12708/122741 ( reposiTUm)
Faustmann, M., Melenk, J. M., & Praetorius, D. (2019). OEMG jahrestagung. OEMG Jahrestagung 2019, Dornbirn, Austria. http://hdl.handle.net/20.500.12708/123160 ( reposiTUm)
Faustmann, M., Melenk, J. M., Parvizi, M., & Praetorius, D. (2019). Optimal adaptivity and preconditioning for the fractional Laplacian. GAMM 2019, Wien, Austria. http://hdl.handle.net/20.500.12708/122727 ( reposiTUm)
Faustmann, M., Melenk, J. M., Parvizi, M., & Praetorius, D. (2019). Optimal adaptivity and preconditioning for the fractional Laplacian. WONAPDE 2019 - Sixth Chilean Workshop on Numerical Analysis of Partial Differential Equations, Concepción, Chile. http://hdl.handle.net/20.500.12708/122720 ( reposiTUm)
Faustmann, M., Melenk, J. M., & Praetorius, D. (2018). Optimal adaptivity for the fractional Laplacian. Universität Bonn, Bonn, Germany, EU. http://hdl.handle.net/20.500.12708/122519 ( reposiTUm)
Faustmann, M., & Melenk, J. M. (2017). Discrete interior regularity and applications. RMMM 8 - Reliable Methods of Mathematical Modeling, Berlin, EU. http://hdl.handle.net/20.500.12708/121891 ( reposiTUm)
Faustmann, M., & Melenk, J. M. (2017). Local convergence of the boundary element method on polyhedral domains. 13th Austrian Numerical Analysis Day, Salzburg, Austria. http://hdl.handle.net/20.500.12708/121853 ( reposiTUm)
Faustmann, M., & Melenk, J. M. (2017). Local convergence of the boundary element method on polyhedral domains. BEM on the Saar 2017, Saarbrücken, EU. http://hdl.handle.net/20.500.12708/121863 ( reposiTUm)
Faustmann, M., Melenk, J. M., & Praetorius, D. (2016). H-matrix approximation to the inverses of BEM matrices. Workshop on Boundary Elements and Adaptivity, Basel, Non-EU. http://hdl.handle.net/20.500.12708/121463 ( reposiTUm)
Faustmann, M., & Melenk, J. M. (2016). Local error estimates and convergence of the Galerkin boundary element method on polygonal domains. MAFELAP 2016 - The Mathematics of Finite Elements and Applications, London, EU. http://hdl.handle.net/20.500.12708/121549 ( reposiTUm)
Faustmann, M., Melenk, J. M., & Praetorius, D. (2015). Existence of H-matrix approximants to the inverse of BEM matrices: the hyper-singular integral operator. 11th Austrian Numerical Analysis, Linz, EU. http://hdl.handle.net/20.500.12708/121106 ( reposiTUm)
Faustmann, M., Melenk, J. M., & Praetorius, D. (2013). Black-box preconditioning of BEM matrices by H-matrix techniques. IABEM 2013 Symposium of the International Association for Boundary Element Methods, Santiago, Non-EU. http://hdl.handle.net/20.500.12708/120244 ( reposiTUm)
Faustmann, M., Melenk, J. M., & Praetorius, D. (2013). Black-Box Preconditioning of FEM/BEM Matrices by H-Matrix Techniques. MAFELAP 2013 - The Mathematics of Finite Elements and Applications, Uxbridge, EU. http://hdl.handle.net/20.500.12708/120341 ( reposiTUm)
Faustmann, M., Melenk, J. M., & Praetorius, D. (2013). H-Matrix approximability of inverse FEM matrices for various boundary conditions. 9th Austrian Numerical Analysis Day, Graz, Austria. http://hdl.handle.net/20.500.12708/120320 ( reposiTUm)
Faustmann, M., Melenk, J. M., & Praetorius, D. (2012). Existence of H-matrix approximants to the inverse of BEM matrices. 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), Wien, Austria. http://hdl.handle.net/20.500.12708/120060 ( reposiTUm)
Faustmann, M., Melenk, J. M., & Praetorius, D. (2012). Existence of H-Matrix Approximants to the Inverse of BEM Matrices. ICOSAHOM 2012, Gammarth, Tunesien, Non-EU. http://hdl.handle.net/20.500.12708/120047 ( reposiTUm)
Faustmann, M., Melenk, J. M., & Praetorius, D. (2012). Existence of H-matrix approximants to inverse BEM matrices. 10th Söllerhaus Workshop on Fast Boundary Element Methods in Industrial Applications, Hirschegg, Austria. http://hdl.handle.net/20.500.12708/120070 ( reposiTUm)

Berichte

Faustmann, M., Melenk, J. M., & Parvizi, M. (2020). On the stability of Scott-Zhang type operators and application to multilevel preconditioning in fractal diffusion (ASC Report 3/2020; pp. 1–31). Institute of Analysis and Scientific Computing, TU Wien. http://hdl.handle.net/20.500.12708/30872 ( reposiTUm)
Angleitner, N., Faustmann, M., & Melenk, J. M. (2020). Approximating inverse FEM matrices on non-uniform meshes with H-matrices (ASC Report 14/2020; pp. 1–21). Institute of Analysis and Scientific Computing, TU Wien. http://hdl.handle.net/20.500.12708/30882 ( reposiTUm)
Faustmann, M., Melenk, J. M., & Parvizi, M. (2020). Caccioppoli-type estimates and H-Matrix approximations to inverses for FEM-BEM coupling (ASC Report 20/2020; pp. 1–31). Institute of Analysis and Scientific Computing, TU Wien. http://hdl.handle.net/20.500.12708/30892 ( reposiTUm)
Faustmann, M., Karkulik, M., & Melenk, J. M. (2020). Local convergence of the FEM for the integral fractional Laplacian (ASC Report 24/2020; pp. 1–20). Institute of Analysis and Scientific Computing, TU Wien. http://hdl.handle.net/20.500.12708/30893 ( reposiTUm)
Faustmann, M., Melenk, J. M., & Praetorius, D. (2019). Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian (ASC Report 07/2019; pp. 1–23). Institute of Analysis and Scientific Computing, TU Wien. http://hdl.handle.net/20.500.12708/30846 ( reposiTUm)
Faustmann, M., & Melenk, J. M. (2017). Local convergence of the boundary element method on polyhedral domains (ASC Report 03/2017; pp. 1–38). Institute of Analysis and Scientific Computing, TU Wien. http://hdl.handle.net/20.500.12708/29363 ( reposiTUm)
Faustmann, M., & Melenk, J. M. (2016). Robust exponential convergence of $hp$-FEM in balanced norms for singularly perturbed reaction-diffusion problems: corner domains (ASC Report 25/2016; pp. 1–17). Institute of Analysis and Scientific Computing, TU Wien. http://hdl.handle.net/20.500.12708/29176 ( reposiTUm)
Faustmann, M., Melenk, J. M., & Praetorius, D. (2015). Existence of $\cal H$-matrix approximants to the inverse of BEM matrices: the hyper-singular integral operator (ASC Report 08/2015; pp. 1–30). Institute of Analysis and Scientific Computing, TU Wien. http://hdl.handle.net/20.500.12708/28605 ( reposiTUm)
Faustmann, M., Melenk, J. M., & Praetorius, D. (2013). Existence of H-matrix approximants to the inverses of BEM matrices: the simple-layer operator (ASC Report 37/2013; pp. 1–33). Institute of Analysis and Scientific Computing, TU Wien. http://hdl.handle.net/20.500.12708/28038 ( reposiTUm)
Faustmann, M., Melenk, J. M., & Praetorius, D. (2013). H-matrix approximability of the inverses of FEM matrices (ASC Report 20/2013; pp. 1–23). Institute of Analysis and Scientific Computing, TU Wien. http://hdl.handle.net/20.500.12708/27971 ( reposiTUm)
Faustmann, M., Melenk, J. M., & Praetorius, D. (2012). A new proof for existence of $\mathcal{H}$-matrix approximants to the inverse of FEM matrices: the Dirichlet problem for the Laplacian (ASC Report 51/2012; pp. 1–10). Institute of Analysis and Scientific Computing, TU Wien. http://hdl.handle.net/20.500.12708/27728 ( reposiTUm)

Hochschulschriften

Faustmann, M. (2015). Approximation inverser Finite Elemente- und Randelementematrizen mittels hierarchischen Matrizen [Dissertation, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2015.31046 ( reposiTUm)
Faustmann, M. (2011). Entropy method and large time behavior of the vorticity equation [Diploma Thesis, Technische Universität Wien]. reposiTUm. http://hdl.handle.net/20.500.12708/160438 ( reposiTUm)