Eli Broad, the wealthy philanthropist who is about to open a major new museum in Los Angeles, is a billionaire straight from central casting. He is a self-made man in the quintessential American industry — home construction — who has also built and burned bridges all across this sprawling city. Ask around, and no one seems to like him, though many call him effective and all agree he is the city’s supremely influential cultural leader, a Tamburlaine of contemporary art. They admire his brilliance, covet his money, fear his power and lament his character, which is described as imperious, egomaniacal and relentless.

On Sunday, Broad and his wife, Edythe, will open the Broad, a $140 million museum that will store and display the Broad Collection, some 2,000 works, with a new one being added, on average, about once a week. Located next to Los Angeles’s iconic landmark of contemporary architecture, the Frank Gehry-designed Walt Disney Concert Hall, the Broad was designed by Diller Scofidio + Renfro, the New York firm that created the High Line park and the Institute of Contemporary Art in Boston and that was slated to design the ill-fated and unrealized temporary “Bubble” space for the Hirshhorn Museum in Washington.

The juxtaposition is striking. Gehry’s Disney Hall is set at an angle to the street, and it shimmers, gleams and curves in all directions, while the Broad faces Grand Avenue squarely with a cool, white, boxlike form covered in what the architects call a “veil” of perforated glass-fiber reinforced concrete. But even more striking than the contrast with the Gehry building is the Broad’s subtle argument with much of recent museum design. The prevailing theology of many public buildings today, including too many museums, is about erasing the line between the city and the structure, so that one feels the excitement of urban energy ever present, even while looking at art. The most salient example is the new Whitney Museum in New York, which makes love to Manhattan so eagerly that one can’t help but gape at the city’s promiscuous ubiquity.

The Broad is more inward-looking and allows for a more contemplative experience. Perhaps without intending to do so, it recaptures some of the spiritual drama of the much-maligned monumental museums of yesteryear: Fundamental to any tour of the Broad is a long escalator ride from the lobby level to the square-acre expanse of open, column-free exhibition space on the third floor. This escalation performs much of the same function as the wide, monumental steps that front many of the museums built a century ago. It separates the visitor from the city and from his cares, cars and concerns; it is a narthex for the age of distraction, allowing the mind to rebirth itself into a state of greater focus and spiritual expectation.

Co-founders of The Broad, Eli and Edythe Broad, in the third-floor galleries. (Elizabeth Daniels /Courtesy of The Broad)

The escalator connects the two essential elements of the building. The “veil” is the exoskeleton, punctured by diagonal cuts and distended windows that look a bit like the webbed packing material that has mercifully replaced Styrofoam peanuts. At street level, the Grand Avenue corners of the veil lift up, recalling the shaved corner of the redesigned Juilliard School at Lincoln Center, another DS+R project. These triangular portals scoop in visitors from the street, who then discover the voluptuously non-Euclidean lobby, a space that feels both subterranean and monumental at the same time, like caverns measureless to man, or the underbelly of some enormous prehistoric mammal.

The undulating ceiling of the lobby is part of what the architects call “the vault.” The Broads have long conceived of their collection as a “lending library” of art, and they wanted that collection stored on site. Ordinarily, that would mean creating a lot of back-of-house space with a storage facility hidden from view.

“We decided to turn that liability into a protagonist,” says Elizabeth Diller, one of the founding partners of DS+R. So the vault became a separate structural element inside the enveloping veil, not just a place to store art, but also a kind of mushroom in a box, overhanging the lobby from a giant cantilever, with the third-floor exhibition hall on the mushroom’s cap.

“You are always in relation to it,” says Diller. “It hovers over you, you shoot through it, you snake back through it and you come back out underneath it.” The museum’s circulation pattern offers visitors glimpses into the vault’s storage space as well, with its sliding racks of art visible from the complex descending staircase that visitors follow after exploring the main gallery on the third floor.

All of this rests on a massive scaffolding that covers a three-floor parking structure. So it is a complex structure with dramatic but strikingly intuitive results. In some ways it recalls Gordon Bunshaft’s Beinecke Library at Yale, where the books are contained in a core glass-lined internal tower, surrounded by a dramatic translucent skin that mediates the light while shutting out the world. It also has affinities with the old Whitney Building, designed by Marcel Breuer, which dramatically invites the visitor to step out of the world so as to see the world, through art, with renewed vigor.

It isn’t, of course, a perfect building. A lecture hall on the second floor feels austere and charmless, and is, surprisingly, the only interior place where one can experience one of the most whimsical features of the building, an oculus that looks from the outside like a thumb print or tiny crater in the veil. But the oculus doesn’t make much sense from inside the lecture hall, which is tiny and dispiriting. And a round elevator, which gives access from the lobby to the third floor, terminates in a distracting glass case in the middle of the main exhibition space.

The Broad’s lobby with escalator. (Iwan Baan/Courtesy of The Broad and Diller Scofidio + Renfro)

The main problem, however, isn’t the building, but the Broad collection itself. More than 250 works are on display, and too many of them are the usual high-end trash. The volume of work chosen for the inaugural exhibition, on both the third floor and a smaller first-floor gallery that will eventually be used for temporary shows, is overwhelming. Partition walls clutter the third floor and obliterate its spatial drama. And too many of the works are so large, and importune the visitor so aggressively, that one feels hectored by hectares of art.

Even though the bad overwhelms the great, there are great works throughout, including a magnificent room devoted to Cy Twombly documenting the arc of his career, iconic Pop works of the 1960s, and compelling art by Ed Ruscha, John Baldessari and Jasper Johns. A room of Ellsworth Kelly is too constrained for the work to have impact, as is a giant piece by Robert Therrien, his 1994 “Under the Table,” which is a Brobdingnagian table and chairs stuffed into a Lilliputian gallery at one corner of the top floor.

Someone has taken care, here and there, to create smart moments amid the clangor, but Jeff Koons always wins. The first gallery encountered has large-scale but effective work by Julie Mehretu, El Anatsui and Mark Bradford, pieces that accentuate the drama of the exterior world you’ve left behind. Mehretu’s “Cairo” (from 2013), recalls the Freudian overlays of history and the unconscious that are the essence of the megalopolis lifestyle; Bradford’s “Corner of Desire and Piety” (2008) refers to the social failures of the Hurricane Katrina catastrophe and by extension the frailty and irrationality of the urban fabric; and the El Anatsui tapestry, “Red Black,” 2010, undulating on the wall, recalls the skin of the museum itself, woven of many pieces, with a curious declivity dramatizing its strength. But a large Jeff Koons piece is droning nearby, vitiating thought with its generic monotone of irony.

A few spaces for video offer relief, including Ragnar Kjartansson’s magnificent “The Visitors,” 2012, and a room devoted to William Kentridge. But video doesn’t seem to be an essential part of this first display; nor are there oases of smaller work or works on paper to modulate the experience. Big is the theme, and it’s exhausting.

So leave the building and lest anyone deprecate it too much — which is inevitable given the local swelling and indigestion that Broad’s name seems to cause in this town — stand at the corner of Grand Avenue and Second Street. Behind you is Gehry’s metal masterpiece; before you is an estimable refusal to be intimidated by it. And if you look down the north face of the building, the angle of the distended cuts in the veil seem to be absorbing the power of the bright blue sky, radiating it down to the ground, while along the Grand Street facade the same energies seem to flow up out of the sidewalk and back to the heavens. The veil has an energy of its own, a force field protecting a dramatic rarity: a space for art that respects the experience of looking and engagement, as a thing apart, and something worth leaving the world behind to do on its own terms.

The Broad, located at 221 S. Grand Ave. in Los Angeles, is scheduled to open to the public on Sept. 20. For more information visit www.thebroad.org.