Mercurial > repos > public > sbplib
view +time/SBPInTime.m @ 1037:2d7ba44340d0 feature/burgers1d
Pass scheme specific parameters as cell array. This will enabale constructDiffOps to be more general. In addition, allow for schemes returning function handles as diffOps, which is currently how non-linear schemes such as Burgers1d are implemented.
author | Vidar Stiernström <vidar.stiernstrom@it.uu.se> |
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date | Fri, 18 Jan 2019 09:02:02 +0100 |
parents | 38173ea263ed |
children | 8894e9c49e40 |
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classdef SBPInTime < time.Timestepper % The SBP in time method. % Implemented for v_t = A*v + f(t) % % Each "step" takes one block step and thus advances % k = k_local*(blockSize-1) in time. properties M % System matrix L,U,P,Q % LU factorization of M A Et_r penalty f k_local % step size within a block k % Time size of a block k/(blockSize-1) = k_local t v m n blockSize % number of points in each block order nodes end methods function obj = SBPInTime(A, f, k, t0, v0, TYPE, order, blockSize) default_arg('TYPE','gauss'); if(strcmp(TYPE,'gauss')) default_arg('order',4) default_arg('blockSize',4) else default_arg('order', 8); default_arg('blockSize',time.SBPInTime.smallestBlockSize(order,TYPE)); end obj.A = A; obj.f = f; obj.k_local = k/(blockSize-1); obj.k = k; obj.blockSize = blockSize; obj.t = t0; obj.m = length(v0); obj.n = 0; %==== Build the time discretization matrix =====% switch TYPE case 'equidistant' ops = sbp.D2Standard(blockSize,{0,obj.k},order); case 'optimal' ops = sbp.D1Nonequidistant(blockSize,{0,obj.k},order); case 'minimal' ops = sbp.D1Nonequidistant(blockSize,{0,obj.k},order,'minimal'); case 'gauss' ops = sbp.D1Gauss(blockSize,{0,obj.k}); end D1 = ops.D1; HI = ops.HI; e_l = ops.e_l; e_r = ops.e_r; obj.nodes = ops.x; Ix = speye(size(A)); It = speye(blockSize,blockSize); obj.Et_r = kron(e_r,Ix); % Time derivative + penalty tau = 1; Mt = D1 + tau*HI*(e_l*e_l'); % penalty to impose "data" penalty = tau*HI*e_l; obj.penalty = kron(penalty,Ix); Mx = kron(It,A); Mt = kron(Mt,Ix); obj.M = Mt - Mx; %==============================================% % LU factorization [obj.L,obj.U,obj.P,obj.Q] = lu(obj.M); % Pretend that the initial condition is the last level % of a previous step. obj.v = 1/(e_r'*e_r) * obj.Et_r * v0; end function [v,t] = getV(obj) v = obj.Et_r' * obj.v; t = obj.t; end function obj = step(obj) obj.v = time.sbp.sbpintime(obj.v, obj.t, obj.nodes,... obj.penalty, obj.f, obj.blockSize,... obj.Et_r,... obj.L, obj.U, obj.P, obj.Q); obj.t = obj.t + obj.k; obj.n = obj.n + 1; end end methods(Static) function N = smallestBlockSize(order,TYPE) default_arg('TYPE','gauss') switch TYPE case 'equidistant' switch order case 2 N = 2; case 4 N = 8; case 6 N = 12; case 8 N = 16; case 10 N = 20; case 12 N = 24; otherwise error('Operator does not exist'); end case 'optimal' switch order case 4 N = 8; case 6 N = 12; case 8 N = 16; case 10 N = 20; case 12 N = 24; otherwise error('Operator does not exist'); end case 'minimal' switch order case 4 N = 6; case 6 N = 10; case 8 N = 12; case 10 N = 16; case 12 N = 20; otherwise error('Operator does not exist'); end case 'gauss' N = 4; end end end end