A new method for periodic scattering problems using 2nd kind boundary integral equations and the free-space Green s function, adding extra degrees of freedom on the unit cell walls, and imposing quasi-periodicity in an expanded linear system. This avoids the problems with the standard approach, namely: the quasi-periodic Green s function is slow to evaluate, it diverges at Wood s anomalies, and it does not handle large aspect ratios well. Our new approach cures all three issues, and can easily be `wrapped around an existing code (e.g. fast-multipole acceleration) for the isolated-obstacle scattering problem. It includes the latest talk slides: "A new integral representation for quasi-periodic scattering problems in two dimensions"

Quasi-periodic scattering problems\@basis\basis.m
..................................\..oundedqpstrip\boundedqpstrip.m
..................................\..vp\bvp.m
..................................\.domain\addconnectedsegs.m
..................................\.......\addcornerbases.m
..................................\.......\addepwbasis.m
..................................\.......\addlayerpot.m
..................................\.......\addmfsbasis.m
..................................\.......\addnufbbasis.m
..................................\.......\addqprayleighbasis.m
..................................\.......\addregfbbasis.m
..................................\.......\addrpwbasis.m
..................................\.......\approxpolygon.m
..................................\.......\domain.m
..................................\.......\evalbases.m
..................................\.......\plot.m
..................................\.......\setrefractiveindex.m
..................................\.......\showdomains.m
..................................\.......\showsegments.m
..................................\.......\stackquadpts.m
..................................\.epwbasis\epwbasis.m
..................................\..vp\evp.m
..................................\....\gridminfit.m
..................................\....\iterparabolafit.m
..................................\....\NtDspectrum.m
..................................\....\para_fit.m
..................................\....\solvebetaode.m
..................................\....\weylcountcheck.m
..................................\.ftylayerpot\ftylayerpot.m
..................................\.layerpot\D.m
..................................\.........\Dkernel.m
..................................\.........\DTkernel.m
..................................\.........\evalfty.m
..................................\.........\fundsol.m
..................................\.........\fundsol_deriv.m
..................................\.........\layerpot.m
..................................\.........\localfromDLP.m
..................................\.........\localfromSLP.m
..................................\.........\S.m
..................................\.........\Skernel.m
..................................\.........\T.m
..................................\.........\Tkernel.m
..................................\.mfsbasis\mfsbasis.m
..................................\.nufbbasis\nufbbasis.m
..................................\.pointset\plot.m
..................................\.........\pointset.m
..................................\..roblem\problem.m
..................................\.qpbstlayerpot\qpbstlayerpot.m
..................................\...ftylayerpot\qpftylayerpot.m
..................................\...rayleighbasis\qprayleighbasis.m
..................................\...scatt\qpscatt.m
..................................\....trip\qpstrip.m
..................................\...uclayerpot\qpuclayerpot.m
..................................\....nitcell\datawrapR.m
..................................\...........\qpunitcell.m
..................................\..uadr\alpertizeselfmatrix.m
..................................\......\clencurt.m
..................................\......\gauss.m
..................................\......\kapurtrap.m
..................................\......\kress_Rjn.m
..................................\......\perispecdiffrow.m
..................................\......\peritrap.m
..................................\......\QuadLogExtraPtNodes.m
..................................\......\QuadNodesInterval.m
..................................\......\QuadNodesIntervalSeq.m
..................................\......\quadr.m
..................................\......\QuadSmoothExtraPtNodes.m
..................................\......\QuadSqrtExtraPtNodes.m
..................................\......\smoothedstep.m
..................................\......\test_Alpert_Pataki.m
..................................\......\test_kapurtrap_Gimbutas.m
.......................

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