sbplib: +sbp/D1Nonequidistant.m annotate

annotate +sbp/D1Nonequidistant.m @ 1198:2924b3a9b921 feature/d2_compatible

Add OpSet for fully compatible D2Variable, created from regular D2Variable by replacing d1 by first row of D1. Formal reduction by one order of accuracy at the boundary point.

author	Martin Almquist <malmquist@stanford.edu>
date	Fri, 16 Aug 2019 14:30:28 -0700
parents	bc78157c89cb
children	4cb627c7fb90

rev	line source
258 a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	1 classdef D1Nonequidistant < sbp.OpSet
a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	2 properties
a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	3 D1 % SBP operator approximating first derivative
a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	4 H % Norm matrix
a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	5 HI % H^-1
a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	6 Q % Skew-symmetric matrix
268 4b9310edcdf8 Renamned boundary operators! Martin Almquist <martin.almquist@it.uu.se> parents: 264 diff changeset	7 e_l % Left boundary operator
4b9310edcdf8 Renamned boundary operators! Martin Almquist <martin.almquist@it.uu.se> parents: 264 diff changeset	8 e_r % Right boundary operator
258 a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	9 m % Number of grid points.
a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	10 h % Step size
a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	11 x % grid
259 a94bb3d92aba Added empty borrowing property to nonequidstant class. Martin Almquist <martin.almquist@it.uu.se> parents: 258 diff changeset	12 borrowing % Struct with borrowing limits for different norm matrices
258 a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	13 end
396 3fdfad20037e Remove whitespace. Jonatan Werpers <jonatan@werpers.com> parents: 268 diff changeset	14
258 a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	15 methods
264 8a625c5a3633 Changed input parameter L (domain length) to lim (cell with domain boundaries) Martin Almquist <martin.almquist@it.uu.se> parents: 262 diff changeset	16 function obj = D1Nonequidistant(m,lim,order,option)
396 3fdfad20037e Remove whitespace. Jonatan Werpers <jonatan@werpers.com> parents: 268 diff changeset	17
258 a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	18 default_arg('option','Accurate');
a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	19 % 'Accurate' operators are optimized for accuracy
a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	20 % 'Minimal' operators have the smallest possible boundary
259 a94bb3d92aba Added empty borrowing property to nonequidstant class. Martin Almquist <martin.almquist@it.uu.se> parents: 258 diff changeset	21 % closure
396 3fdfad20037e Remove whitespace. Jonatan Werpers <jonatan@werpers.com> parents: 268 diff changeset	22
264 8a625c5a3633 Changed input parameter L (domain length) to lim (cell with domain boundaries) Martin Almquist <martin.almquist@it.uu.se> parents: 262 diff changeset	23 x_l = lim{1};
8a625c5a3633 Changed input parameter L (domain length) to lim (cell with domain boundaries) Martin Almquist <martin.almquist@it.uu.se> parents: 262 diff changeset	24 x_r = lim{2};
8a625c5a3633 Changed input parameter L (domain length) to lim (cell with domain boundaries) Martin Almquist <martin.almquist@it.uu.se> parents: 262 diff changeset	25 L = x_r-x_l;
396 3fdfad20037e Remove whitespace. Jonatan Werpers <jonatan@werpers.com> parents: 268 diff changeset	26
258 a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	27 switch option
396 3fdfad20037e Remove whitespace. Jonatan Werpers <jonatan@werpers.com> parents: 268 diff changeset	28
258 a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	29 case {'Accurate','accurate','A'}
396 3fdfad20037e Remove whitespace. Jonatan Werpers <jonatan@werpers.com> parents: 268 diff changeset	30
258 a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	31 if order == 4
261 6009f2712d13 Moved and renamned all implementations. Martin Almquist <martin.almquist@it.uu.se> parents: 259 diff changeset	32 [obj.D1,obj.H,obj.x,obj.h] = ...
6009f2712d13 Moved and renamned all implementations. Martin Almquist <martin.almquist@it.uu.se> parents: 259 diff changeset	33 sbp.implementations.d1_noneq_4(m,L);
258 a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	34 elseif order == 6
261 6009f2712d13 Moved and renamned all implementations. Martin Almquist <martin.almquist@it.uu.se> parents: 259 diff changeset	35 [obj.D1,obj.H,obj.x,obj.h] = ...
6009f2712d13 Moved and renamned all implementations. Martin Almquist <martin.almquist@it.uu.se> parents: 259 diff changeset	36 sbp.implementations.d1_noneq_6(m,L);
258 a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	37 elseif order == 8
261 6009f2712d13 Moved and renamned all implementations. Martin Almquist <martin.almquist@it.uu.se> parents: 259 diff changeset	38 [obj.D1,obj.H,obj.x,obj.h] = ...
6009f2712d13 Moved and renamned all implementations. Martin Almquist <martin.almquist@it.uu.se> parents: 259 diff changeset	39 sbp.implementations.d1_noneq_8(m,L);
258 a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	40 elseif order == 10
261 6009f2712d13 Moved and renamned all implementations. Martin Almquist <martin.almquist@it.uu.se> parents: 259 diff changeset	41 [obj.D1,obj.H,obj.x,obj.h] = ...
6009f2712d13 Moved and renamned all implementations. Martin Almquist <martin.almquist@it.uu.se> parents: 259 diff changeset	42 sbp.implementations.d1_noneq_10(m,L);
258 a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	43 elseif order == 12
261 6009f2712d13 Moved and renamned all implementations. Martin Almquist <martin.almquist@it.uu.se> parents: 259 diff changeset	44 [obj.D1,obj.H,obj.x,obj.h] = ...
6009f2712d13 Moved and renamned all implementations. Martin Almquist <martin.almquist@it.uu.se> parents: 259 diff changeset	45 sbp.implementations.d1_noneq_12(m,L);
258 a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	46 else
a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	47 error('Invalid operator order %d.',order);
a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	48 end
396 3fdfad20037e Remove whitespace. Jonatan Werpers <jonatan@werpers.com> parents: 268 diff changeset	49
258 a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	50 case {'Minimal','minimal','M'}
396 3fdfad20037e Remove whitespace. Jonatan Werpers <jonatan@werpers.com> parents: 268 diff changeset	51
258 a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	52 if order == 4
261 6009f2712d13 Moved and renamned all implementations. Martin Almquist <martin.almquist@it.uu.se> parents: 259 diff changeset	53 [obj.D1,obj.H,obj.x,obj.h] = ...
6009f2712d13 Moved and renamned all implementations. Martin Almquist <martin.almquist@it.uu.se> parents: 259 diff changeset	54 sbp.implementations.d1_noneq_minimal_4(m,L);
258 a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	55 elseif order == 6
261 6009f2712d13 Moved and renamned all implementations. Martin Almquist <martin.almquist@it.uu.se> parents: 259 diff changeset	56 [obj.D1,obj.H,obj.x,obj.h] = ...
6009f2712d13 Moved and renamned all implementations. Martin Almquist <martin.almquist@it.uu.se> parents: 259 diff changeset	57 sbp.implementations.d1_noneq_minimal_6(m,L);
258 a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	58 elseif order == 8
261 6009f2712d13 Moved and renamned all implementations. Martin Almquist <martin.almquist@it.uu.se> parents: 259 diff changeset	59 [obj.D1,obj.H,obj.x,obj.h] = ...
6009f2712d13 Moved and renamned all implementations. Martin Almquist <martin.almquist@it.uu.se> parents: 259 diff changeset	60 sbp.implementations.d1_noneq_minimal_8(m,L);
258 a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	61 elseif order == 10
261 6009f2712d13 Moved and renamned all implementations. Martin Almquist <martin.almquist@it.uu.se> parents: 259 diff changeset	62 [obj.D1,obj.H,obj.x,obj.h] = ...
6009f2712d13 Moved and renamned all implementations. Martin Almquist <martin.almquist@it.uu.se> parents: 259 diff changeset	63 sbp.implementations.d1_noneq_minimal_10(m,L);
258 a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	64 elseif order == 12
261 6009f2712d13 Moved and renamned all implementations. Martin Almquist <martin.almquist@it.uu.se> parents: 259 diff changeset	65 [obj.D1,obj.H,obj.x,obj.h] = ...
6009f2712d13 Moved and renamned all implementations. Martin Almquist <martin.almquist@it.uu.se> parents: 259 diff changeset	66 sbp.implementations.d1_noneq_minimal_12(m,L);
258 a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	67 else
a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	68 error('Invalid operator order %d.',order);
a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	69 end
396 3fdfad20037e Remove whitespace. Jonatan Werpers <jonatan@werpers.com> parents: 268 diff changeset	70
258 a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	71 end
396 3fdfad20037e Remove whitespace. Jonatan Werpers <jonatan@werpers.com> parents: 268 diff changeset	72
264 8a625c5a3633 Changed input parameter L (domain length) to lim (cell with domain boundaries) Martin Almquist <martin.almquist@it.uu.se> parents: 262 diff changeset	73 obj.x = obj.x + x_l;
396 3fdfad20037e Remove whitespace. Jonatan Werpers <jonatan@werpers.com> parents: 268 diff changeset	74
268 4b9310edcdf8 Renamned boundary operators! Martin Almquist <martin.almquist@it.uu.se> parents: 264 diff changeset	75 obj.e_l = sparse(m,1);
4b9310edcdf8 Renamned boundary operators! Martin Almquist <martin.almquist@it.uu.se> parents: 264 diff changeset	76 obj.e_r = sparse(m,1);
4b9310edcdf8 Renamned boundary operators! Martin Almquist <martin.almquist@it.uu.se> parents: 264 diff changeset	77 obj.e_l(1) = 1;
4b9310edcdf8 Renamned boundary operators! Martin Almquist <martin.almquist@it.uu.se> parents: 264 diff changeset	78 obj.e_r(m) = 1;
396 3fdfad20037e Remove whitespace. Jonatan Werpers <jonatan@werpers.com> parents: 268 diff changeset	79
258 a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	80 obj.HI = inv(obj.H);
268 4b9310edcdf8 Renamned boundary operators! Martin Almquist <martin.almquist@it.uu.se> parents: 264 diff changeset	81 obj.Q = obj.Hobj.D1 - obj.e_robj.e_r' + obj.e_l*obj.e_l';
396 3fdfad20037e Remove whitespace. Jonatan Werpers <jonatan@werpers.com> parents: 268 diff changeset	82
259 a94bb3d92aba Added empty borrowing property to nonequidstant class. Martin Almquist <martin.almquist@it.uu.se> parents: 258 diff changeset	83 obj.borrowing = [];
402 bc78157c89cb Add string methods to some sbp classes. Jonatan Werpers <jonatan@werpers.com> parents: 397 diff changeset	84
bc78157c89cb Add string methods to some sbp classes. Jonatan Werpers <jonatan@werpers.com> parents: 397 diff changeset	85 end
bc78157c89cb Add string methods to some sbp classes. Jonatan Werpers <jonatan@werpers.com> parents: 397 diff changeset	86
bc78157c89cb Add string methods to some sbp classes. Jonatan Werpers <jonatan@werpers.com> parents: 397 diff changeset	87 function str = string(obj)
bc78157c89cb Add string methods to some sbp classes. Jonatan Werpers <jonatan@werpers.com> parents: 397 diff changeset	88 str = [class(obj) '_' num2str(obj.order)];
258 a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	89 end
a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	90 end
a8d89688ba01 Merged nonequidistant into one class and cleaned up. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	91 end

Mercurial > repos > public > sbplib

annotate +sbp/D1Nonequidistant.m @ 1198:2924b3a9b921 feature/d2_compatible