A computer-implemented method for multi-scale modeling, comprising: obtaining a model of a subterranean domain, the model comprising a plurality of fine cells and a plurality of subdomains, wherein each subdomain of the plurality of subdomains comprise two or more of the plurality of fine cells; determining a first matrix for the plurality of fine cells based at least in part on a physical property value represented by respective fine cells of the plurality of fine cells; identifying one or more overlapped cells of the plurality of fine cells, wherein each of the one or more overlapped cells is part of at least two of the plurality of subdomains; determining , using a processor, a second matrix, comprising: determining an intermediate product by multiplying the first matrix by a prolongation matrix, wherein determining the intermediate product comprises setting a row of the intermediate product to all zeros without conducting matrix multiplication operations, wherein the row corresponds to a plurality of fine cells that are not the one or more overlapped cells and are not part of the at least two of the plurality of subdomains that include the one or more overlapped cells; and multiplying the intermediate product by a restriction matrix to generate the second matrix; and adjusting the model based at least partially on the second matrix. obtaining a model of a subterranean domain, the model comprising a plurality of fine cells and a plurality of subdomains, wherein each subdomain of the plurality of subdomains comprise two or more of the plurality of fine cells; determining a first matrix for the plurality of fine cells based at least in part on a physical property value represented by respective fine cells of the plurality of fine cells; identifying one or more overlapped cells of the plurality of fine cells, wherein each of the one or more overlapped cells is part of at least two of the plurality of subdomains; determining , using a processor, a second matrix, comprising: determining an intermediate product by multiplying the first matrix by a prolongation matrix, wherein determining the intermediate product comprises setting a row of the intermediate product to all zeros without conducting matrix multiplication operations, wherein the row corresponds to a plurality of fine cells that are not the one or more overlapped cells and are not part of the at least two of the plurality of subdomains that include the one or more overlapped cells; and multiplying the intermediate product by a restriction matrix to generate the second matrix; and determining an intermediate product by multiplying the first matrix by a prolongation matrix, wherein determining the intermediate product comprises setting a row of the intermediate product to all zeros without conducting matrix multiplication operations, wherein the row corresponds to a plurality of fine cells that are not the one or more overlapped cells and are not part of the at least two of the plurality of subdomains that include the one or more overlapped cells; and multiplying the intermediate product by a restriction matrix to generate the second matrix; and adjusting the model based at least partially on the second matrix. <EOS>