def norm(p, arg, dd=None):
"""
:arg arg: is assumed to be a vector, i.e. have shape ``(n,)``.
"""
sym = _sym()
if dd is None:
dd = sym.DD_VOLUME
dd = sym.as_dofdesc(dd)
if p == 2:
norm_squared = sym.NodalSum(dd_in=dd)(
sym.FunctionSymbol("fabs")(
arg * sym.MassOperator()(arg)))
if isinstance(norm_squared, np.ndarray):
norm_squared = norm_squared.sum()
return sym.FunctionSymbol("sqrt")(norm_squared)
elif p == np.Inf:
result = sym.NodalMax(dd_in=dd)(sym.FunctionSymbol("fabs")(arg))
from pymbolic.primitives import Max
if isinstance(result, np.ndarray):
from functools import reduce
result = reduce(Max, result)
return result
else:
raise ValueError("unsupported value of p")
def max_eigenvalue_expr(self):
"""Return the largest eigenvalue of Maxwell's equations as a hyperbolic
system.
"""
from math import sqrt
if self.fixed_material:
return 1/sqrt(self.epsilon*self.mu) # a number
else:
import grudge.symbolic as sym
return sym.NodalMax()(1/sym.FunctionSymbol("sqrt")(self.epsilon*self.mu))
def max_eigenvalue(self, t, fields=None, discr=None):
return sym.NodalMax()(sym.FunctionSymbol("fabs")(self.c))
def max_eigenvalue(self, t, fields=None, discr=None):
return sym.NodalMax("vol")(sym.fabs(self.c))