1)原始Jacobi迭代，收敛挺好的。 init ok! it= 100, real error=1.666565, matrix error=0.010373 it= 200, real error=1.339508, matrix error=0.004651 it= 300, real error=1.136802, matrix error=0.002839 it= 400, real error=0.993261, matrix error=0.001976 it= 500, real error=0.881123, matrix error=0.001483 it= 600, real error=0.788313, matrix error=0.001170 it= 700, real error=0.706898, matrix error=0.000962 it= 800, real error=0.633495, matrix error=0.000815 it= 900, real error=0.566826, matrix error=0.000705 it=1000, real error=0.506387, matrix error=0.000619 it=1100, real error=0.451818, matrix error=0.000546 it=1200, real error=0.402616, matrix error=0.000484 it=1300, real error=0.358500, matrix error=0.000429 it=1400, real error=0.319111, matrix error=0.000381 it=1500, real error=0.283842, matrix error=0.000338 it=1600, real error=0.252400, matrix error=0.000300 it=1700, real error=0.224579, matrix error=0.000266 it=1800, real error=0.199754, matrix error=0.000236 it=1900, real error=0.177632, matrix error=0.000210 it=2000, real error=0.157939, matrix error=0.000186 it=2100, real error=0.140438, matrix error=0.000165 it=2200, real error=0.124890, matrix error=0.000147 it=2300, real error=0.111116, matrix error=0.000131 it=2400, real error=0.098856, matrix error=0.000116 it=2500, real error=0.087946, matrix error=0.000103 it=2600, real error=0.078238, matrix error=0.000092 it=2700, real error=0.069601, matrix error=0.000082 it=2800, real error=0.061918, matrix error=0.000072 it=2900, real error=0.055083, matrix error=0.000064 it=3000, real error=0.049002, matrix error=0.000057 it=3100, real error=0.043594, matrix error=0.000051 it=3200, real error=0.038782, matrix error=0.000045 it=3300, real error=0.034502, matrix error=0.000040 it=3400, real error=0.030694, matrix error=0.000036 it=3500, real error=0.027307, matrix error=0.000032 it=3600, real error=0.024294, matrix error=0.000028 it=3700, real error=0.021614, matrix error=0.000025 it=3800, real error=0.019229, matrix error=0.000022 it=3900, real error=0.017107, matrix error=0.000020 it=4000, real error=0.015220, matrix error=0.000018 it=4100, real error=0.013541, matrix error=0.000016 it=4200, real error=0.012047, matrix error=0.000014 it=4300, real error=0.010718, matrix error=0.000013 it=4400, real error=0.009536, matrix error=0.000011 it=4500, real error=0.008484, matrix error=0.000010 it=4600, real error=0.007548, matrix error=0.000009 it=4700, real error=0.006716, matrix error=0.000008 it=4800, real error=0.005975, matrix error=0.000007 it=4900, real error=0.005316, matrix error=0.000006 it=5000, real error=0.004730, matrix error=0.000006 Time: 137.088s global max error = 0.004730 2） 加了自认为 的correct后，速度慢，且发散了 init ok! it= 100, real error=1.596056, matrix error=1.235165 it= 200, real error=1.207422, matrix error=1.235229 it= 300, real error=0.948430, matrix error=1.235239 it= 400, real error=0.752270, matrix error=1.235242 it= 500, real error=0.672308, matrix error=1.235243 it= 600, real error=0.672074, matrix error=1.235243 it= 700, real error=0.671922, matrix error=1.235244 it= 800, real error=0.671817, matrix error=1.235244 it= 900, real error=0.671741, matrix error=1.235244 it=1000, real error=0.671684, matrix error=1.235244 it=1100, real error=0.671639, matrix error=1.235244 it=1200, real error=0.671604, matrix error=1.235244 it=1300, real error=0.671575, matrix error=1.235244 it=1400, real error=0.671552, matrix error=1.235244 it=1500, real error=0.671532, matrix error=1.235244 it=1600, real error=0.671515, matrix error=1.235244 it=1700, real error=0.671501, matrix error=1.235244 it=1800, real error=0.671489, matrix error=1.235244 it=1900, real error=0.671479, matrix error=1.235244 it=2000, real error=0.671470, matrix error=1.235244 it=2100, real error=0.671463, matrix error=1.235244 it=2200, real error=0.671456, matrix error=1.235244 it=2300, real error=0.671450, matrix error=1.235244 it=2400, real error=0.671445, matrix error=1.235244 it=2500, real error=0.671441, matrix error=1.235244 it=2600, real error=0.682293, matrix error=1.235244 it=2700, real error=0.695402, matrix error=1.235244 it=2800, real error=0.707053, matrix error=1.235244 it=2900, real error=0.717408, matrix error=1.235244 it=3000, real error=0.726621, matrix error=1.235244 it=3100, real error=0.734912, matrix error=1.235244 it=3200, real error=0.742282, matrix error=1.235244 it=3300, real error=0.748835, matrix error=1.235244 it=3400, real error=0.754662, matrix error=1.235244 it=3500, real error=0.759842, matrix error=1.235244 it=3600, real error=0.764449, matrix error=1.235244 it=3700, real error=0.768545, matrix error=1.235244 it=3800, real error=0.772188, matrix error=1.235244 it=3900, real error=0.775427, matrix error=1.235244 it=4000, real error=0.778308, matrix error=1.235244 it=4100, real error=0.780869, matrix error=1.235244 it=4200, real error=0.783148, matrix error=1.235244 it=4300, real error=0.785174, matrix error=1.235244 it=4400, real error=0.786976, matrix error=1.235244 it=4500, real error=0.788578, matrix error=1.235244 it=4600, real error=0.790004, matrix error=1.235244 it=4700, real error=0.791272, matrix error=1.235244 it=4800, real error=0.792399, matrix error=1.235244 it=4900, real error=0.793402, matrix error=1.235244 it=5000, real error=0.794294, matrix error=1.235244 Time: 403.488s global max error = 1.580396 for(i=1; i<=N-2; i++) for(j=1; j<=N-2; j++) for(k=1; k<=N-2; k++) { R1[i][j][k] =A[i][j][k] - B[i][j][k]; } 3） for(i=1; i<=N-2; i++) for(j=1; j<=N-2; j++) for(k=1; k<=N-2; k++) { //R1[i][j][k] =A[i][j][k] - B[i][j][k]; R1[i][j][k] = (A[i-1][j][k]+A[i+1][j][k]+A[i][j-1][k]+A[i][j+1][k]+A[i][j][k-1]+A[i][j][k+1] -6*A[i][j][k] - F[i][j][k]*dxyz*dxyz); } init ok! it= 100, real error=1116241435711945121564693890686914761414148677023705317166739464503937486039800283321124341983425331200.000000, matrix error=2224682862064052040830095112834993306872665090893115309201935421926064282899029131562835876919346462720.000000 it= 200, real error=291033708157889013266078360170225726593135232358558800823170683057032249174792667468046776639417686069834836645800190750054065740723722821098430291387127374342879484160823797575771127159488781324562828342350315520.000000, matrix error=580800869713372115889902522737091066998755697112839447856971829797420225696625978720738509093511954704676743711780868669833625888411540762583757883853043837910055474224873836327251390996805674900233897072731881472.000000 it= 300, real error=nan, matrix error=nan it= 400, real error=nan, matrix error=nan 直接NAN了 4) for(i=1; i<=N-2; i++) for(j=1; j<=N-2; j++) for(k=1; k<=N-2; k++) { //R1[i][j][k] =A[i][j][k] - B[i][j][k]; R1[i][j][k] = (A[i-1][j][k]+A[i+1][j][k]+A[i][j-1][k]+A[i][j+1][k]+A[i][j][k-1]+A[i][j][k+1] -6*A[i][j][k])/(dxyz*dxyz) - F[i][j][k]; } 更加发散了 init ok! it= 100, real error=nan, matrix error=nan it= 200, real error=nan, matrix error=nan it= 300, real error=nan, matrix error=nan it= 400, real error=nan, matrix error=nan 5） 可能还是要用多重网格的方法，粗化可以消除低频误差 6） 由于多重网格能够有效提高数值计算的计算效率、以及通过不同层的网格实现消除误差的有点，被广泛应用于流体动力学问题，特别是对N-S方程组( Navier-Stokes equations)的数值求解。目前很多的商业软件采用了多重网格算法(multigrid algorithm)，例如Fluent、Comsol、Star ccm+等。 Fluent包含代数多重网格（Algebraic Multigrid，AMG）和全近似存储（Full-Approximation Storage ，FAS）多重网格两类多重网格方法，其中代数多重网格是用于隐式求解器，而全近似存储多重网格则用于显式求解器，当然实际使用中标量的求解应该使用的是代数多重网格。全近似存储（Full-Approximation Storage ，FAS）多重网格又可以被称为几何多重网格，几何多重网格需要对粗网格进行构建和存储来获得“粗”方程组，而代数多重网格获得“粗”方程组无需使用任何几何或在粗网格上重新离散化。 7） 多重网格算法是一种迭代算法，其基本思想是：在不同规模网格上求解同一个问题，细网格负责消除误差的高频分量，而误差低频分量的消除则由粗网格负责完成，细网格光滑、粗网格校正、嵌套迭代技术是该算法的三个关键点，在细网格上作光滑迭代消除误差的高频分量，然后对误差的低频分量在更粗网格上进行校正，嵌套迭代技术通过限制和延拓算子连接所有层共同求解同一个问题，细网格光淆与粗网格校正过程的有机结合构成了多重网格 这个写得好！ |
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