_-Ph><dZddlZddlmZejdz ddfdZdS)zQGenerate matrix and right-hand side for upwind FD discretization of 2D advection.N) stencil_gridg@g?c ttdkrtd|dks|tjdz krtdtj|}tj|}tjgd| ||zdgd| dgg}t| }tjfdtddD}tjfdtddD} tj || f fd td|j dD} tj |rtjd|}n&|j ddkrtd tj |rtjd|}n&|j ddkrtd tj ||f} || d d fd d  f | z} || d d fd d | f}|| fS) am Generate matrix and RHS for upwind FD discretization of 2D advection. (cos(theta),sin(theta)) dot grad(u) = 0, with inflow boundaries on the left and bottom of the domain. Assume uniform grid spacing, dx=dy, even for grid[0] != grid[1]. Parameters ---------- grid : tuple (ny, nx) number of points in y and x theta : float, optional Rotation angle `theta` in radians defines direction of advection (cos(theta),sin(theta)) l_bdry : float, array left boundary value. If float, then constant in-flow boundary value applied. If array, then length of array must be equal to ny = grid[0], and this array defines non-constant boundary value on the left. b_bdry : float, array bottom boundary value. If float, then constant in-flow boundary value applied. If array, then length of array must be equal to nx = grid[1], and this array defines non-constant boundary value on the bottom. Returns ------- A : csr_matrix Defines 2D FD upwind discretization, with boundary rhs : array Defines right-hand-side with boundary contributions See Also -------- poisson Examples -------- >>> from numpy import pi >>> from pyamg.gallery import advection_2d >>> A, rhs = advection_2d( (4,4), theta=pi/4) >>> print(A.toarray().round(4)) [[ 1.4142 0. 0. -0.7071 0. 0. 0. 0. 0. ] [-0.7071 1.4142 0. 0. -0.7071 0. 0. 0. 0. ] [ 0. -0.7071 1.4142 0. 0. -0.7071 0. 0. 0. ] [ 0. 0. 0. 1.4142 0. 0. -0.7071 0. 0. ] [ 0. 0. 0. -0.7071 1.4142 0. 0. -0.7071 0. ] [ 0. 0. 0. 0. -0.7071 1.4142 0. 0. -0.7071] [ 0. 0. 0. 0. 0. 0. 1.4142 0. 0. ] [ 0. 0. 0. 0. 0. 0. -0.7071 1.4142 0. ] [ 0. 0. 0. 0. 0. 0. 0. -0.7071 1.4142]] zCgrid must be a length 2 tuple, describe number of points in x and yrztheta must be in (0, pi/2))rrrc&g|] }|dzS)r.0igrids W/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/pyamg/gallery/advection.py z advection_2d..Ns!===a$q' ===c>g|]}dddz z|zS)rrrr s r rz advection_2d..Os/III!Qa+A-IIIrrcg|]}|v| Srr)r r all_bdofss r rz advection_2d..Qs#FFFa1I3E3E3E3E3Erz/left boundary data does not match boundary sizez1bottom boundary data does not match boundary sizeN)tuplelen ValueErrornppicossinarrayrtocsrrange concatenateshapeisscalarfullflatten)r thetal_bdryb_bdryw1w2stAl_bdofsb_bdofsint_dofsbdryrhsrs` @r advection_2dr.sj ;;D 4yyA~~@AA A zzUbeAg%%5666 B B 999sBrE1oB3{; < >GhIIIIuQQ7H7HIIIJJG122IFFFF5AGAJ//FFFH {6La&)) aDG # #JKKK {6Na&)) aDG # #LMMM >6>>++V^^-=-=> ? ?D Xqqq[>!!!Y, ' ' ,C (AAA+qqq({#A c6Mr)__doc__numpyrstencilrrr.rrr r2s\WW!!!!!! U3Ys3\\\\\\r