def elliptic_oned_demo(args): args['PROBLEM-NUMBER'] = int(args['PROBLEM-NUMBER']) assert 0 <= args['PROBLEM-NUMBER'] <= 1, ValueError('Invalid problem number.') args['N'] = int(args['N']) rhss = [GenericFunction(lambda X: np.ones(X.shape[:-1]) * 10, dim_domain=1), GenericFunction(lambda X: (X[..., 0] - 0.5) ** 2 * 1000, dim_domain=1)] rhs = rhss[args['PROBLEM-NUMBER']] d0 = GenericFunction(lambda X: 1 - X[..., 0], dim_domain=1) d1 = GenericFunction(lambda X: X[..., 0], dim_domain=1) parameter_space = CubicParameterSpace({'diffusionl': 0}, 0.1, 1) f0 = ProjectionParameterFunctional('diffusionl', 0) f1 = GenericParameterFunctional(lambda mu: 1, {}) print('Solving on OnedGrid(({0},{0}))'.format(args['N'])) print('Setup Problem ...') problem = EllipticProblem(domain=LineDomain(), rhs=rhs, diffusion_functions=(d0, d1), diffusion_functionals=(f0, f1), dirichlet_data=ConstantFunction(value=0, dim_domain=1), name='1DProblem') print('Discretize ...') discretizer = discretize_elliptic_fv if args['--fv'] else discretize_elliptic_cg discretization, _ = discretizer(problem, diameter=1 / args['N']) print('The parameter type is {}'.format(discretization.parameter_type)) U = discretization.solution_space.empty() for mu in parameter_space.sample_uniformly(10): U.append(discretization.solve(mu)) print('Plot ...') discretization.visualize(U, title='Solution for diffusionl in [0.1, 1]')
def elliptic_oned_demo(args): args['PROBLEM-NUMBER'] = int(args['PROBLEM-NUMBER']) assert 0 <= args['PROBLEM-NUMBER'] <= 1, ValueError('Invalid problem number.') args['N'] = int(args['N']) rhss = [ExpressionFunction('ones(x.shape[:-1]) * 10', 1, ()), ExpressionFunction('(x - 0.5)**2 * 1000', 1, ())] rhs = rhss[args['PROBLEM-NUMBER']] d0 = ExpressionFunction('1 - x', 1, ()) d1 = ExpressionFunction('x', 1, ()) parameter_space = CubicParameterSpace({'diffusionl': 0}, 0.1, 1) f0 = ProjectionParameterFunctional('diffusionl', 0) f1 = ExpressionParameterFunctional('1', {}) problem = StationaryProblem( domain=LineDomain(), rhs=rhs, diffusion=LincombFunction([d0, d1], [f0, f1]), dirichlet_data=ConstantFunction(value=0, dim_domain=1), name='1DProblem' ) print('Discretize ...') discretizer = discretize_stationary_fv if args['--fv'] else discretize_stationary_cg d, data = discretizer(problem, diameter=1 / args['N']) print(data['grid']) print() print('Solve ...') U = d.solution_space.empty() for mu in parameter_space.sample_uniformly(10): U.append(d.solve(mu)) d.visualize(U, title='Solution for diffusionl in [0.1, 1]')