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An Exponentially Convergent Nonpolynomial Finite Element Method for Time-Harmonic Scattering from Polygons

A. H. Barnett, T. Betcke
2010 SIAM Journal on Scientific Computing  
We present and analyze such a method for the scattering of two-dimensional scalar waves from a polygonal domain that achieves exponential convergence purely by increasing the number of basis functions  ...  In recent years nonpolynomial finite element methods have received increasing attention for the efficient solution of wave problems.  ...  MPSpack example: scattering from a square.  ... 
doi:10.1137/090768667 fatcat:ouyspffc7bentmykg6oaecv4d4

Propagation Methods for Quantum Molecular Dynamics

R Kosloff
1994 Annual review of physical chemistry (Print)  
The introduction of pseudo-spectral methods has been an important step in this direction.  ...  These methods allow an extremely accurate representation of the action of an operator, usually the Hamiltonian, on a wavefunction: q~ = fI~p.  ...  The convergence is exponential with the relaxation constant approximately as predicted from Equation 7.14, for an harmonic oscillator of frequency 1.  ... 
doi:10.1146/annurev.physchem.45.1.145 fatcat:itb7otvv4vhbjpmzd2a5746qny

Propagation Methods for Quantum Molecular Dynamics

R Kosloff
1994 Annual review of physical chemistry (Print)  
The introduction of pseudo-spectral methods has been an important step in this direction.  ...  These methods allow an extremely accurate representation of the action of an operator, usually the Hamiltonian, on a wavefunction: q~ = fI~p.  ...  The convergence is exponential with the relaxation constant approximately as predicted from Equation 7.14, for an harmonic oscillator of frequency 1.  ... 
doi:10.1146/annurev.pc.45.100194.001045 fatcat:aw4m5a3zc5hjxdgvummgy7o5da

Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks [article]

N. Sukumar, Ankit Srivastava
2021 arXiv   pre-print
To this end, we use concepts from constructive solid geometry (R-functions) and generalized barycentric coordinates (mean value potential fields) to construct ϕ, an approximate distance function to the  ...  In doing so, we eliminate modeling error associated with the satisfaction of boundary conditions in a collocation method and ensure that kinematic admissibility is met pointwise in a Ritz method.  ...  On a square, there exists an exact solution for this problem-harmonic coordinates coincide with bilinear finite element shape functions.  ... 
arXiv:2104.08426v2 fatcat:6ihxtxwkunczvoixtb46juyrue

Shaping dynamics with multiple populations in low-rank recurrent networks [article]

Manuel Beiran, Alexis Dubreuil, Adrian Valente, Francesca Mastrogiuseppe, Srdjan Ostojic
2020 arXiv   pre-print
An emerging paradigm proposes that neural computations can be understood at the level of dynamical systems that govern low-dimensional trajectories of collective neural activity.  ...  We thank Mehrdad Jazayeri and Eli Pollock for discussions. Code availability Code and trained models will be made available upon publication.  ...  Secondly, we determine the statistics of the left connectivity patterns and the external input, by drawing random values for the mean values in each population a I 2 from an exponential distribution,  ... 
arXiv:2007.02062v2 fatcat:sj2jz2wyevcmnkkm5xi2hrkxom

Lectures on 2D gravity and 2D string theory (TASI 1992) [article]

P. Ginsparg, Gregory Moore
1993 arXiv   pre-print
String scattering in two spacetime dimensions 14. Vertex Operator Calculations and Continuum Methods 15.  ...  Matrix Model Technology I: Method of Orthogonal Polynomials 8. Matrix Model Technology II: Loops on the Lattice 9. Matrix Model Technology III: Free Fermions from the Lattice 10.  ...  The idea is based on the remark that the contribution of a hole with a finite lattice size, or a surface with a finite number of polygons, to (8.7) will always be analytic in ζ, V .  ... 
arXiv:hep-th/9304011v1 fatcat:mfmwllkwjrcihjbo4uikypcsny

Introduction to AdS-CFT [article]

Horatiu Nastase
2007 arXiv   pre-print
, finite temperature and scattering processes, the pp wave correspondence and spin chains.  ...  basic methods.  ...  It takes a finite time for a light ray to go to the boundary of AdS space, since ds 2 = 0 implies dt = ∞ dU/U 2 =finite.  ... 
arXiv:0712.0689v2 fatcat:ssaxwbgqazhv7gmn7xfc6wazfu

Critical phenomena and renormalization-group theory

Andrea Pelissetto, Ettore Vicari
2002 Physics reports  
The results for the tetragonal Hamiltonian are original, in particular we present the six-loop perturbative series for the β-functions.  ...  Finally, we consider a Hamiltonian with symmetry O(n_1)⊕ O(n_2) that is relevant for the description of multicritical phenomena.  ...  The variational method transforms an initially divergent series in a convergent sequence of approximations.  ... 
doi:10.1016/s0370-1573(02)00219-3 fatcat:cdjf66ynovevdczzvfkjww73pi

Field Theories of Interacting and Disordered Dirac Fermions in Graphene [article]

Christian Fräßdorf, Universitätsbibliothek Der FU Berlin, Universitätsbibliothek Der FU Berlin
2019
To circumvent some of the technical problems of the standard fRG formalism when treating fermionic systems at finite density, we also explore a variant of the fRG, where the chemical potential is interpreted  ...  functions, we construct a nonperturbative formalism for the calculation of these vertex functions using the well-established functional renormalization group (fRG).  ...  She stood by me for a long time now with love, support and encouragement. Her good spirit cheered me up in hard times and stimulated me to keep going.  ... 
doi:10.17169/refubium-2153 fatcat:c4iqmiixljanpng7xyz657fzze

Modular radiance transfer

Bradford J. Loos
2016
a t e S c h o o l STATEMENT OF DISSERTATION APPROVAL The dissertation of B r a d fo rd J L o o s has been approved by the following supervisory committee members: P e te r-P ik e S loan C h a rles H an  ...  Spherical harmonic exponentiation [20] defines blocker geometry as spherical harmonic coefficients.  ...  These allow more complicated visibility functions but still can be simply combined using spherical harmonic exponentiation.  ... 
doi:10.26053/0h-xt7h-y900 fatcat:angtatl6xfazxmibi2gjtgx6fi