  In this paper, we design and analyze two new methods based on additive
average Schwarz -- AAS method introduced in \cite{MR1943457}. The new methods
design for elliptic problems with highly heterogeneous coefficients. The
methods are of the non-overlapping type, and the subdomain interactions obtain
via the coarse space. The first method is the minimum energy Schwarz -- MES
method. MES has the minimum energy for the coarse space with constant extension
inside each subdomain. The condition number of the MES method is always smaller
than in the AAS method. The second class of methods is the non-overlapping
spectral additive Schwarz -- NOSAS methods based on low-rank discrete energy
harmonic extension in each subdomain. To achieve the low-rank, we solve a
generalized eigenvalue problem in each subdomain. NOSAS have the minimum energy
for a given rank of the coarse space. The condition number of the NOSAS methods
does not depend on the coefficients. Additionally, the NOSAS methods have good
parallelization properties. The size of the global problem is equal to the
total number of eigenvalues chosen in each subdomain. It is only related to the
number of high-permeable islands that touch the subdomains' interface.
