| 7 |
- Projector - to project a discontinuous |
- Projector - to project a discontinuous |
| 8 |
- Locator - to trace values in data objects at a certain location |
- Locator - to trace values in data objects at a certain location |
| 9 |
- TimeIntegrationManager - to handel extraplotion in time |
- TimeIntegrationManager - to handel extraplotion in time |
| 10 |
|
- SaddlePointProblem - solver for Saddle point problems using the inexact uszawa scheme |
| 11 |
|
|
| 12 |
@var __author__: name of author |
@var __author__: name of author |
| 13 |
@var __copyright__: copyrights |
@var __copyright__: copyrights |
| 354 |
else: |
else: |
| 355 |
return data |
return data |
| 356 |
|
|
| 357 |
|
class SaddlePointProblem(object): |
| 358 |
|
""" |
| 359 |
|
This implements a solver for a saddlepoint problem |
| 360 |
|
|
| 361 |
|
f(u,p)=0 |
| 362 |
|
g(u)=0 |
| 363 |
|
|
| 364 |
|
for u and p. The problem is solved with an inexact Uszawa scheme for p: |
| 365 |
|
|
| 366 |
|
Q_f (u^{k+1}-u^{k}) = - f(u^{k},p^{k}) |
| 367 |
|
Q_g (p^{k+1}-p^{k}) = g(u^{k+1}) |
| 368 |
|
|
| 369 |
|
where Q_f is an approximation of the Jacobiean A_f of f with respect to u and Q_f is an approximation of |
| 370 |
|
A_g A_f^{-1} A_g with A_g is the jacobiean of g with respect to p. As a the construction of a 'proper' |
| 371 |
|
Q_g can be difficult, non-linear conjugate gradient method is applied to solve for p, so Q_g plays |
| 372 |
|
in fact the role of a preconditioner. |
| 373 |
|
""" |
| 374 |
|
def __init__(self,verbose=False,*args): |
| 375 |
|
""" |
| 376 |
|
initializes the problem |
| 377 |
|
|
| 378 |
|
@parm verbose: switches on the printing out some information |
| 379 |
|
@type verbose: C{bool} |
| 380 |
|
@note: this method may be overwritten by a particular saddle point problem |
| 381 |
|
""" |
| 382 |
|
self.__verbose=verbose |
| 383 |
|
|
| 384 |
|
def trace(self,text): |
| 385 |
|
""" |
| 386 |
|
prints text if verbose has been set |
| 387 |
|
|
| 388 |
|
@parm text: a text message |
| 389 |
|
@type text: C{str} |
| 390 |
|
""" |
| 391 |
|
if self.__verbose: print "%s: %s"%(str(self),text) |
| 392 |
|
|
| 393 |
|
def solve_f(self,u,p,tol=1.e-7,*args): |
| 394 |
|
""" |
| 395 |
|
solves |
| 396 |
|
|
| 397 |
|
A_f du = f(u,p) |
| 398 |
|
|
| 399 |
|
with tolerance C{tol} and return du. A_f is Jacobiean of f with respect to u. |
| 400 |
|
|
| 401 |
|
@param u: current approximation of u |
| 402 |
|
@type u: L{escript.Data} |
| 403 |
|
@param p: current approximation of p |
| 404 |
|
@type p: L{escript.Data} |
| 405 |
|
@param tol: tolerance for du |
| 406 |
|
@type tol: C{float} |
| 407 |
|
@return: increment du |
| 408 |
|
@rtype: L{escript.Data} |
| 409 |
|
@note: this method has to be overwritten by a particular saddle point problem |
| 410 |
|
""" |
| 411 |
|
pass |
| 412 |
|
|
| 413 |
|
def solve_g(self,u,*args): |
| 414 |
|
""" |
| 415 |
|
solves |
| 416 |
|
|
| 417 |
|
Q_g dp = g(u) |
| 418 |
|
|
| 419 |
|
with Q_g is a preconditioner for A_g A_f^{-1} A_g with A_g is the jacobiean of g with respect to p. |
| 420 |
|
|
| 421 |
|
@param u: current approximation of u |
| 422 |
|
@type u: L{escript.Data} |
| 423 |
|
@return: increment dp |
| 424 |
|
@rtype: L{escript.Data} |
| 425 |
|
@note: this method has to be overwritten by a particular saddle point problem |
| 426 |
|
""" |
| 427 |
|
pass |
| 428 |
|
|
| 429 |
|
def inner(self,p0,p1): |
| 430 |
|
""" |
| 431 |
|
inner product of p0 and p1 approximating p. Typically this returns integrate(p0*p1) |
| 432 |
|
@return: inner product of p0 and p1 |
| 433 |
|
@rtype: C{float} |
| 434 |
|
""" |
| 435 |
|
pass |
| 436 |
|
|
| 437 |
|
def solve(self,u0,p0,tolerance=1.e-6,*args): |
| 438 |
|
pass |
| 439 |
# vim: expandtab shiftwidth=4: |
# vim: expandtab shiftwidth=4: |
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