Kuzmin, Dmitri; Bäcker, Jan-Phillip An unfitted finite element method using level set functions for extrapolation into deformable diffuse interfaces. (English) Zbl 07525184 J. Comput. Phys. 461, Article ID 111218, 16 p. (2022). MSC: 65Nxx 76Mxx 65Mxx PDFBibTeX XMLCite \textit{D. Kuzmin} and \textit{J.-P. Bäcker}, J. Comput. Phys. 461, Article ID 111218, 16 p. (2022; Zbl 07525184) Full Text: DOI arXiv
Zhang, Tiankui; Wolgemuth, Charles W. A general computational framework for the dynamics of single- and multi-phase vesicles and membranes. (English) Zbl 07517106 J. Comput. Phys. 450, Article ID 110815, 30 p. (2022). MSC: 65Mxx 65Dxx 92Cxx PDFBibTeX XMLCite \textit{T. Zhang} and \textit{C. W. Wolgemuth}, J. Comput. Phys. 450, Article ID 110815, 30 p. (2022; Zbl 07517106) Full Text: DOI
Saye, Robert I. High-order quadrature on multi-component domains implicitly defined by multivariate polynomials. (English) Zbl 07516804 J. Comput. Phys. 448, Article ID 110720, 31 p. (2022). MSC: 65Dxx 65Nxx 41Axx PDFBibTeX XMLCite \textit{R. I. Saye}, J. Comput. Phys. 448, Article ID 110720, 31 p. (2022; Zbl 07516804) Full Text: DOI arXiv
Tsao, Bing-Jyun; Haas, Roland; Tsokaros, Antonios Source term method for binary neutron stars initial data. (English) Zbl 1481.85001 Classical Quantum Gravity 38, No. 13, Article ID 135008, 23 p. (2021). MSC: 85A05 58J47 58J32 70F05 35J05 35Q05 65F10 PDFBibTeX XMLCite \textit{B.-J. Tsao} et al., Classical Quantum Gravity 38, No. 13, Article ID 135008, 23 p. (2021; Zbl 1481.85001) Full Text: DOI arXiv
Zhang, Tiankui; Wolgemuth, Charles W. Sixth-order accurate schemes for reinitialization and extrapolation in the level set framework. (English) Zbl 1437.65116 J. Sci. Comput. 83, No. 2, Paper No. 26, 21 p. (2020). MSC: 65M06 35F21 35R37 PDFBibTeX XMLCite \textit{T. Zhang} and \textit{C. W. Wolgemuth}, J. Sci. Comput. 83, No. 2, Paper No. 26, 21 p. (2020; Zbl 1437.65116) Full Text: DOI
Bochkov, Daniil; Gibou, Frederic Solving Poisson-type equations with Robin boundary conditions on piecewise smooth interfaces. (English) Zbl 1416.65409 J. Comput. Phys. 376, 1156-1198 (2019). MSC: 65N08 35J25 PDFBibTeX XMLCite \textit{D. Bochkov} and \textit{F. Gibou}, J. Comput. Phys. 376, 1156--1198 (2019; Zbl 1416.65409) Full Text: DOI
Towers, John D. A source term method for Poisson problems on irregular domains. (English) Zbl 1422.65327 J. Comput. Phys. 361, 424-441 (2018). MSC: 65N06 35J05 PDFBibTeX XMLCite \textit{J. D. Towers}, J. Comput. Phys. 361, 424--441 (2018; Zbl 1422.65327) Full Text: DOI
Kublik, Catherine; Tsai, Richard An extrapolative approach to integration over hypersurfaces in the level set framework. (English) Zbl 1391.65047 Math. Comput. 87, No. 313, 2365-2392 (2018). Reviewer: Adhemar Bultheel (Leuven) MSC: 65D30 PDFBibTeX XMLCite \textit{C. Kublik} and \textit{R. Tsai}, Math. Comput. 87, No. 313, 2365--2392 (2018; Zbl 1391.65047) Full Text: DOI arXiv
Egan, Raphael; Gibou, Frédéric Geometric discretization of the multidimensional Dirac delta distribution – application to the Poisson equation with singular source terms. (English) Zbl 1380.65349 J. Comput. Phys. 346, 71-90 (2017). MSC: 65N22 35J05 35A08 65D30 PDFBibTeX XMLCite \textit{R. Egan} and \textit{F. Gibou}, J. Comput. Phys. 346, 71--90 (2017; Zbl 1380.65349) Full Text: DOI
Kublik, Catherine; Tsai, Richard Integration over curves and surfaces defined by the closest point mapping. (English) Zbl 1336.65021 Res. Math. Sci. 3, Paper No. 3, 17 p. (2016). MSC: 65D30 PDFBibTeX XMLCite \textit{C. Kublik} and \textit{R. Tsai}, Res. Math. Sci. 3, Paper No. 3, 17 p. (2016; Zbl 1336.65021) Full Text: DOI arXiv
Saye, R. I. High-order quadrature methods for implicitly defined surfaces and volumes in hyperrectangles. (English) Zbl 1328.65070 SIAM J. Sci. Comput. 37, No. 2, A993-A1019 (2015). MSC: 65D30 65N30 PDFBibTeX XMLCite \textit{R. I. Saye}, SIAM J. Sci. Comput. 37, No. 2, A993--A1019 (2015; Zbl 1328.65070) Full Text: DOI Link
Müller, B.; Kummer, F.; Oberlack, M. Highly accurate surface and volume integration on implicit domains by means of moment-fitting. (English) Zbl 1352.65083 Int. J. Numer. Methods Eng. 96, No. 8, 512-528 (2013). MSC: 65D30 65N30 PDFBibTeX XMLCite \textit{B. Müller} et al., Int. J. Numer. Methods Eng. 96, No. 8, 512--528 (2013; Zbl 1352.65083) Full Text: DOI
Kublik, Catherine; Tanushev, Nicolay M.; Tsai, Richard An implicit interface boundary integral method for Poisson’s equation on arbitrary domains. (English) Zbl 1349.65661 J. Comput. Phys. 247, 279-311 (2013). MSC: 65N38 35J25 PDFBibTeX XMLCite \textit{C. Kublik} et al., J. Comput. Phys. 247, 279--311 (2013; Zbl 1349.65661) Full Text: DOI
Bukshtynov, Vladislav; Protas, Bartosz Optimal reconstruction of material properties in complex multiphysics phenomena. (English) Zbl 1427.80016 J. Comput. Phys. 242, 889-914 (2013). MSC: 80A23 80A20 80M50 65K10 76D05 65M32 65J20 65M55 PDFBibTeX XMLCite \textit{V. Bukshtynov} and \textit{B. Protas}, J. Comput. Phys. 242, 889--914 (2013; Zbl 1427.80016) Full Text: DOI arXiv
Müller, B.; Kummer, F.; Oberlack, M.; Wang, Y. Simple multidimensional integration of discontinuous functions with application to level set methods. (English) Zbl 1352.65084 Int. J. Numer. Methods Eng. 92, No. 7, 637-651 (2012). MSC: 65D30 65N30 PDFBibTeX XMLCite \textit{B. Müller} et al., Int. J. Numer. Methods Eng. 92, No. 7, 637--651 (2012; Zbl 1352.65084) Full Text: DOI
Lee, Hyun Geun; Kim, Junseok Regularized Dirac delta functions for phase field models. (English) Zbl 1246.76148 Int. J. Numer. Methods Eng. 91, No. 3, 269-288 (2012). MSC: 76T99 76M25 PDFBibTeX XMLCite \textit{H. G. Lee} and \textit{J. Kim}, Int. J. Numer. Methods Eng. 91, No. 3, 269--288 (2012; Zbl 1246.76148) Full Text: DOI
Wen, Xin A high order numerical method for computing physical observables in the semiclassical limit of the one-dimensional linear Schrödinger equation with discontinuous potentials. (English) Zbl 1203.65216 J. Sci. Comput. 42, No. 2, 318-344 (2010). MSC: 65M99 35Q40 PDFBibTeX XMLCite \textit{X. Wen}, J. Sci. Comput. 42, No. 2, 318--344 (2010; Zbl 1203.65216) Full Text: DOI
Zahedi, Sara; Tornberg, Anna-Karin Delta function approximations in level set methods by distance function extension. (English) Zbl 1186.65018 J. Comput. Phys. 229, No. 6, 2199-2219 (2010). MSC: 65D15 PDFBibTeX XMLCite \textit{S. Zahedi} and \textit{A.-K. Tornberg}, J. Comput. Phys. 229, No. 6, 2199--2219 (2010; Zbl 1186.65018) Full Text: DOI
Wen, Xin High order numerical methods to two dimensional delta function integrals in level set methods. (English) Zbl 1167.65008 J. Comput. Phys. 228, No. 11, 4273-4290 (2009). Reviewer: Martin D. Buhmann (Gießen) MSC: 65D15 46F10 PDFBibTeX XMLCite \textit{X. Wen}, J. Comput. Phys. 228, No. 11, 4273--4290 (2009; Zbl 1167.65008) Full Text: DOI
Towers, John D. Discretizing delta functions via finite differences and gradient normalization. (English) Zbl 1167.65007 J. Comput. Phys. 228, No. 10, 3816-3836 (2009). Reviewer: Martin D. Buhmann (Gießen) MSC: 65D15 46F10 PDFBibTeX XMLCite \textit{J. D. Towers}, J. Comput. Phys. 228, No. 10, 3816--3836 (2009; Zbl 1167.65007) Full Text: DOI
Liu, Hailiang; Wang, Zhongming Superposition of multi-valued solutions in high frequency wave dynamics. (English) Zbl 1203.65141 J. Sci. Comput. 35, No. 2-3, 192-218 (2008). MSC: 65M06 35F20 76M25 PDFBibTeX XMLCite \textit{H. Liu} and \textit{Z. Wang}, J. Sci. Comput. 35, No. 2--3, 192--218 (2008; Zbl 1203.65141) Full Text: DOI
Towers, John D. Finite difference methods for approximating Heaviside functions. (English) Zbl 1171.65014 J. Comput. Phys. 228, No. 9, 3478-3489 (2009). Reviewer: Jesus Illán González (Vigo) MSC: 65D32 41A55 41A25 41A63 PDFBibTeX XMLCite \textit{J. D. Towers}, J. Comput. Phys. 228, No. 9, 3478--3489 (2008; Zbl 1171.65014) Full Text: DOI
Min, Chohong; Gibou, Frédéric Robust second-order accurate discretizations of the multi-dimensional Heaviside and Dirac delta functions. (English) Zbl 1153.65014 J. Comput. Phys. 227, No. 22, 9686-9695 (2008). MSC: 65D15 PDFBibTeX XMLCite \textit{C. Min} and \textit{F. Gibou}, J. Comput. Phys. 227, No. 22, 9686--9695 (2008; Zbl 1153.65014) Full Text: DOI
Towers, John D. A convergence rate theorem for finite difference approximations to delta functions. (English) Zbl 1155.65016 J. Comput. Phys. 227, No. 13, 6591-6597 (2008). Reviewer: Vasilis Dimitriou (Chania) MSC: 65D15 PDFBibTeX XMLCite \textit{J. D. Towers}, J. Comput. Phys. 227, No. 13, 6591--6597 (2008; Zbl 1155.65016) Full Text: DOI
Beale, J. Thomas A proof that a discrete delta function is second-order accurate. (English) Zbl 1136.65017 J. Comput. Phys. 227, No. 4, 2195-2197 (2008). MSC: 65D15 46F10 PDFBibTeX XMLCite \textit{J. T. Beale}, J. Comput. Phys. 227, No. 4, 2195--2197 (2008; Zbl 1136.65017) Full Text: DOI
Wen, Xin High order numerical methods to a type of delta function integrals. (English) Zbl 1125.65024 J. Comput. Phys. 226, No. 2, 1952-1967 (2007). MSC: 65D32 41A55 41A63 PDFBibTeX XMLCite \textit{X. Wen}, J. Comput. Phys. 226, No. 2, 1952--1967 (2007; Zbl 1125.65024) Full Text: DOI